Question

A right triangle has a hypotenuse whose length is 26 inches and a leg whose length is 10 inches which of the following is the area of the right triangle in square inches

Answer 1

check the picture below.

Answer 2

Given the following data:

• Hypotenuse of right triangle = 26 inches

• Adjacent of right triangle = 10 inches

To find the area of the right triangle in square inches:

First of all, we would determine the other leg (opposite side) of the right triangle by using the Pythagorean's theorem.

Mathematically, Pythagorean's theorem is calculated by using the formula:

$C^2 = A^2 + B^2$

Where:

• C is the hypotenuse.

• A is the opposite side.

• B is the adjacent side.

Substituting the values into the formula, we have:

$26^2 = A^2 + 10^2\\\\676 = A^2 + 100\\\\A^2 = 676 - 100\\\\A^2 = 576\\\\A = \sqrt{576}$

A = 24 millimeters.

Now, we would solve for the area of the right triangle by using the formula:

$Area = \frac{1}{2}$ × $base$ × $height$

$Area = \frac{1}{2}$ × $10$ × $24$

$Area = 5$  × $24$

Area = 120 square inches.

Therefore, the area of the right triangle in square inches is 120.

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