Solve Applications of Quadratic Equations

Question

A rectangle is drawn so the width is 4 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.

Answer 1

about 17

h=17, w=21

17^2 +21^2 = 289+441 = 730= about 27^2 = 729

h^2 + (4+h)^2 = 27^2

2h^2 + 8h +16 = 729

h^2 + 4h -713/2 = 0

h =-4/2 + (1/2)sqr(16+4(713/2))= about 18.9-2 = 16.9 or about 17 = height