Question

A rectangle is drawn so the width is 5 inches longer than

the height. If the rectangle's diagonal measurement is 36
inches, find the height.
Give your answer rounded to 1 decimal place.
inches

Answer 1

`length = l\\width = 5 + l\\Diagonal = 36\\diagonal^2 = (5+l)^2 + l^2\\36^2 = 25 + l^2 +10l + l^2\\1296 = 2l^2 +10l +25 \\2l^2 +10l=1271\\\\l_1=(-10+2√(2567))/(2\cdot \:2),\:l_2=(-10-2√(2567))/(2\cdot \:2)`

`l_1=(-5+√(2567))/(2),\:l_2=(-5-√(2567))/(2)`

clearly,

`l_(2) \ is \ a \ negative\ number`

So we consider

`l_(1) =(-5+√(2567))/(2) = 22.83`

Therefore height = 22.8inches