Question

Rectangle ABCD and right triangle DCE have the same area. They are joined to form a trapezoid, as shown. What is DE?

Answer 1

Since the areas are the same (5 x 6 = 30 units), and the height of the triangle (DC) is 5 so the length of the triangle must be 12. (1/2 of 5 x 12 is also 30)

So now we use the Pythagorean theorem

a² + b² = c² we have 5² + 12² = c² or 25 + 144 = c² or 169 = c²

The square root of 169 is 13 so side DE is 13 units.