Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Geometric Mean in Right Triangles — Easy Worksheet 2
Grade 10 · MathSheets 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 = √(18 · 8) = √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 = √(18 · 8) = √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.
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(75 × 12) = √900 = 30. The geometric mean is 30.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(75 × 12) = √900 = 30. The geometric mean is 30.
💡 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 = √(16 · 9) = √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 = √(16 · 9) = √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.
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(2 × 32) = √64 = 8. The geometric mean is 8.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(2 × 32) = √64 = 8. The geometric mean is 8.
💡 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 = √(25 · 16) = √400 = 20. So x = 20.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(25 · 16) = √400 = 20. So x = 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 92 = 27 · x. Then 81 = 27x, so x = 81 ÷ 27 = 3.
✓ Correct!
Not quite. The answer is
💡 The altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so 92 = 27 · x. Then 81 = 27x, so x = 81 ÷ 27 = 3.
💡 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: √(12 × 48) = √576 = 24. The geometric mean is 24.
✓ Correct!
Not quite. The answer is
💡 The geometric mean of two numbers is the square root of their product: √(12 × 48) = √576 = 24. The geometric mean is 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 altitude to the hypotenuse is the geometric mean of the two segments: CD2 = AD · DB, so x = √(8 · 18) = √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 = √(8 · 18) = √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.
Log in to save your progress.
Geometric Mean in Right Triangles — Easy Worksheet 2
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.