If the lengths of the legs of a right triangle are 9 and 12, what is the perimet

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Question: If the lengths of the legs of a right triangle are 9 and 12, what is the perimeter of the triangle?

Options:

Correct Answer: 32

Solution:

Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15. Perimeter = 9 + 12 + 15 = 36.

If the lengths of the legs of a right triangle are 9 and 12, what is the perimeter of the triangle?

If the lengths of the legs of a right triangle are 9 and 12, what is the perimeter of the triangle?

Step 1: Identify the lengths of the legs of the right triangle. They are 9 and 12.
Step 2: Use the Pythagorean theorem to find the length of the hypotenuse. The formula is hypotenuse = √(leg1² + leg2²).
Step 3: Calculate leg1², which is 9² = 81.
Step 4: Calculate leg2², which is 12² = 144.
Step 5: Add the squares of the legs together: 81 + 144 = 225.
Step 6: Take the square root of 225 to find the hypotenuse: √225 = 15.
Step 7: Now, add the lengths of the three sides to find the perimeter: 9 + 12 + 15.
Step 8: Calculate the perimeter: 9 + 12 = 21, then 21 + 15 = 36.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Perimeter Calculation – The perimeter of a triangle is the sum of the lengths of all its sides.