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?
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.