Question

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.
Which equation can be used to find the dimensions of the patio?

0.5(x)(x + 5) = 29
0.5(x)(x + 5) = 841
x2 + (x + 5)2 = 29
x2 + (x + 5)2 = 841

Answer 1

The sides and diagonal of a rectangle form a right triangle. The Pythagorean theorem can be used to relate the dimensions of that triangle. The legs are x and x+5; the hypotenuse is 29. We know 29²=841, so the Pythagorean theorem tells you

... x² + (x+5)² = 841 . . . . . matches the last choice