For ΔABC shown below, base AC has a length of 16 inches

For ΔABC shown below, base AC has a length of 16 inches and altitude BD has a length of 8 inches. The area of a certain square is equal to the area of ΔABC. What is the length, in inches, of a side of the square?

1. 6
2. 8
3. 12
4. 16
5. 32

Answer

The correct answer is B.

The area of a triangle is found by multiplying 1/2 by the length of its altitude, h, and by the length of its base, b. For ΔABC, the length of the altitude is 8 inches and the length of the base is 16 inches.

Therefore, the area of ΔABC is 64 square inches.

Area = 1/2 × 8 × 16 = 64

The area of a square with side length a inches is a².

a2 = 64

a = 8

Thus, the length of a side of the square is 8 inches.