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Grade 10 Quiz: Ratios & Proportions — Easy Version 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Triangle Proportionality & Angle Bisector Theorems: DE ∥ BC. Find x.
Answer: 3
Not quite. The answer is
💡 The labelled edges are 2 and 4, so the scale factor from smaller to larger is k = 42 = 2. Surface areas grow by the square of the scale factor, k2 = 4. Larger surface area = 8 × 4 = 32.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 2 and 4, so the scale factor from smaller to larger is k = 42 = 2. Surface areas grow by the square of the scale factor, k2 = 4. Larger surface area = 8 × 4 = 32.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 5. By what number is its surface area multiplied?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 6x = 32. Cross-multiply: 3x = 6 × 2 = 12. Divide both sides by 3: x = 4.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 6x = 32. Cross-multiply: 3x = 6 × 2 = 12. Divide both sides by 3: x = 4.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The scale factor is 5. Surface area grows by the square of the scale factor: 52 = 5 × 5 = 25. The surface area is multiplied by 25.
✓ Correct!
Not quite. The answer is
💡 The scale factor is 5. Surface area grows by the square of the scale factor: 52 = 5 × 5 = 25. The surface area is multiplied by 25.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 2. By what number is its surface area multiplied?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 106 = 30x. Cross-multiply: 10x = 6 × 30 = 180. Divide both sides by 10: x = 18.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 106 = 30x. Cross-multiply: 10x = 6 × 30 = 180. Divide both sides by 10: x = 18.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The labelled edges are 2 and 6, so the scale factor from smaller to larger is k = 62 = 3. Volumes grow by the cube of the scale factor, k3 = 27. Larger volume = 6 × 27 = 162.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 2 and 6, so the scale factor from smaller to larger is k = 62 = 3. Volumes grow by the cube of the scale factor, k3 = 27. Larger volume = 6 × 27 = 162.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 3. By what number is its surface area multiplied?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 39 = x6. Cross-multiply: 9x = 3 × 6 = 18. Divide both sides by 9: x = 2.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Proportionality Theorem, DE ∥ BC divides the sides proportionally: AD/DB = AE/EC, so 39 = x6. Cross-multiply: 9x = 3 × 6 = 18. Divide both sides by 9: x = 2.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The scale factor is 4. Surface area grows by the square of the scale factor: 42 = 4 × 4 = 16. The surface area is multiplied by 16.
✓ Correct!
Not quite. The answer is
💡 The scale factor is 4. Surface area grows by the square of the scale factor: 42 = 4 × 4 = 16. The surface area is multiplied by 16.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 3. By what number is its surface area multiplied?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 129 = 20x. Cross-multiply: 12x = 9 × 20 = 180. Divide both sides by 12: x = 15.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 129 = 20x. Cross-multiply: 12x = 9 × 20 = 180. Divide both sides by 12: x = 15.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The labelled edges are 2 and 6, so the scale factor from smaller to larger is k = 62 = 3. Surface areas grow by the square of the scale factor, k2 = 9. Larger surface area = 9 × 9 = 81.
✓ Correct!
Not quite. The answer is
💡 The labelled edges are 2 and 6, so the scale factor from smaller to larger is k = 62 = 3. Surface areas grow by the square of the scale factor, k2 = 9. Larger surface area = 9 × 9 = 81.
💡 How to solve: Scale Factor: Effect on Area & Volume
If the scale factor of lengths is ab, then the ratio of areas (including surface areas) is a2/b2 and the ratio of volumes is a3/b3. To go backwards, take the square root of an area ratio or the cube root of a volume ratio to get the length ratio. When every dimension is multiplied by k, area is multiplied by k2 and volume by k3.
Try a similar one
Every dimension of a rectangular prism is multiplied by 5. By what number is its surface area multiplied?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 21 = 4x. Cross-multiply: 2x = 1 × 4 = 4. Divide both sides by 2: x = 2.
✓ Correct!
Not quite. The answer is
💡 By the Triangle Angle Bisector Theorem, AD divides BC in the ratio of the other two sides: BD/DC = AB/AC, so 21 = 4x. Cross-multiply: 2x = 1 × 4 = 4. Divide both sides by 2: x = 2.
💡 How to solve: Triangle Proportionality & Angle Bisector Theorems
If DE is parallel to BC, it divides the two sides proportionally: AD/DB = AE/EC. If AD bisects ∠A of △ABC, it divides BC in the ratio of the other two sides: BD/DC = AB/AC. Write the proportion, cross-multiply and solve.
Try a similar one
DE ∥ BC. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 10 Quiz: Ratios & Proportions — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.