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Geometric Mean in Right Triangles — Easy Worksheet 1
Grade 10 · Whoobee Name: ____________________ Date: __________
In each diagram, △ABC has a right angle at C and CD is the altitude to the hypotenuse. Write answers in simplest radical form when needed.
How to solve
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Example
Find x.
Answer: 6
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(8 · 32) = √256 = 16. So x = 16.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(8 · 32) = √256 = 16. So x = 16.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 geometric mean of two numbers is the square root of their product: √(75 × 108) = √8100 = 90. The geometric mean is 90.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(75 × 108) = √8100 = 90. The geometric mean is 90.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(48 · 12) = √576 = 24. So x = 24.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(48 · 12) = √576 = 24. So x = 24.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 geometric mean of two numbers is the square root of their product: √(27 × 3) = √81 = 9. The geometric mean is 9.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(27 × 3) = √81 = 9. The geometric mean is 9.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(3 · 27) = √81 = 9. So x = 9.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(3 · 27) = √81 = 9. So x = 9.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so 82 = 16 · x. Then 64 = 16x, so x = 64 ÷ 16 = 4.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so 82 = 16 · x. Then 64 = 16x, so x = 64 ÷ 16 = 4.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 geometric mean of two numbers is the square root of their product: √(50 × 8) = √400 = 20. The geometric mean is 20.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(50 × 8) = √400 = 20. The geometric mean is 20.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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 altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(9 · 16) = √144 = 12. So x = 12.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(9 · 16) = √144 = 12. So x = 12.
💡 How to solve: Geometric Mean in Right Triangles
The geometric mean of a and b is √(ab). The altitude to the hypotenuse is the geometric mean of the two hypotenuse segments: CD2 = AD · DB. Each leg is the geometric mean of the whole hypotenuse and the segment next to it: AC2 = AD · AB and BC2 = DB · AB. Multiply, then take the square root and simplify.
Try a similar one
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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Geometric Mean in Right Triangles — Easy Worksheet 1
In each diagram, △ABC has a right angle at C and CD is the altitude to the hypotenuse. Write answers in simplest radical form when needed.