Question

A rectangle is drawn so the width is 97 inches longer than the height. If the rectangle's diagonal measurement is 113 inches, find the height. Give your answer rounded to 1 decimal place. Inches

Answer 1

Step-by-step explanation:

h = height of rectangle (should be "length", but ok)

w = width of rectangle

w = h + 97

the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.

so, we use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle).

diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²

113² = 12769 = 2h² + 194h + 9409

3360 = 2h² + 194h

1680 = h² + 97h = (h + 97/2)² - 9409/4

(completing the square)

6720/4 + 9409/4 = (h + 97/2)²

16129/4 = (h + 97/2)²

127/2 = h + 97/2

30/2 = h = 15

the height is 15.0 in