Question

Two sides of a right triangle are 8” and 12”.

A. Find the the area of the triangle if 8 and 12 are legs.

B. Find the area of the triangle if 8 and 12 are a leg and hypotenuse.

Answer 1

The area of the triangle with legs of 8 inches and 12 inches is 48 square inches. If 8 and 12 are the leg and hypotenuse, the area cannot be determined without the length of the other leg.

Step-by-step explanation:

To find the area of a right triangle, we can use the formula A = (1/2) * base * height. In this case, the base is 8 inches and the height is 12 inches. So the area of the triangle is A = (1/2) * 8 * 12 = 48 square inches.

If 8 and 12 are the length of a leg and the hypotenuse, we cannot directly find the area of the triangle using these values. We would need the length of the other leg to calculate the area.

Answer 2

Area of a right triangle = ab/2

where a and b are both legs of the triangle.

A) a = 8 inches ; b = 12 inches
A = (8in x 12in)/2 = 96/2 = 48 in²

B.) a = 8 inches ; b = ? ; hypotenuse = 12 inches

Pythagorean theorem is used to get the measurement of the hypotenuse. It can also be used to get the measurement of the missing leg.

a² + b² = c² ⇒ b² = c² - a²
b² = 12² - 8²
b² = 144 - 64
b² = 80
b = √80
b = 8.94

A = ab/2 ⇒ (8 inches * 8.94 inches)/2
A = 71.52 in² / 2
A = 35.76 in²