Question

A right triangle has a hypotenuse whose length is 26 inches and a leg whose length is 10 inches. What is the area of the right triangle in square inches?

A) 120 square inches.
B) 130 square inches.
C) 140 square inches.
D) 150 square inches.

Answer 1

Using the Pythagorean theorem, the missing leg of the right triangle is calculated to be 24 inches. The area is then found using the formula for the area of a triangle, yielding an area of 120 square inches, which is option A.

Step-by-step explanation:

To find the area of a right triangle when you have the length of one leg and the hypotenuse, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem is stated as a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the triangle's legs.

First, we find the length of the unknown leg (let's call this b):

• a² + b² = c²
• 10² + b² = 26²
• 100 + b² = 676
• b² = 676 - 100
• b² = 576
• b = √576
• b = 24 inches

Now we use the formula for the area of a triangle (Area = 1/2 × base × height) to find the area. In this case, one leg (10 inches) will be the base, and the other leg (24 inches) will be the height:

• Area = 1/2 × 10 × 24
• Area = 5 × 24
• Area = 120 square inches

So, the area of the right triangle is 120 square inches, which corresponds to option A.

Answer 2

The area of the right triangle is 120 square inches when the length of the hypotenuse is 26 inches and the length of one leg is 10 inches.

Step-by-step explanation:

To find the area of a right triangle, you can use the formula A = 1/2 * base * height.

In this case, the leg of the triangle is given as 10 inches. Let's assume it is the base. The hypotenuse is given as 26 inches.

Using the Pythagorean theorem, we can find the height:

height = sqrt(hypotenuse^2 - base^2) = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 inches

Now, we can find the area:

Area = 1/2 * base * height = 1/2 * 10 * 24 = 120 square inches