Question

The area of a square is 14 times as large as the area of a triangle. One side of the triangle is 7 inches long, and the altitude to that side is the same length as a side of the square. Find the length of a side of the square. Also find the areas of both figures, and be sure that your answer checks.

Answer 1

L^2 = area of square = As

As = 14 L H / 2 where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7 or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2 area of square

H = 7 height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2 Seems to checkout