A rectangle is drawn so the width is 4 inches longer than the height if the rectangle’s diagonal measurement is 20 inches find the height give your answer rounded to 1 decimal place

Question

Find all real solutions to the equation 3r square -12=7r square 3-28r

Answer 1

Height = H in

Width = H + 4 in

Diagonal = 20 in

Use pythagorian theorem for the diagonal

H² + (H + 4)² = 20²

H² + H² + 8H + 16 = 400

2H² + 8H - 384 = 0

Divide by 2: H² + 4H - 192 = 0

(H + 16)(H - 12) = 0 so H = -16 (n.g.) or H = 12 (OK)

Ht = 12 in; Width = 16 in (No rounding required)

Check: 12² + 16² = 20² 144 + 256 = 400 It's a 3:4:5 right triangle!