Question

The base of a triangle exceeds the height by 4 feet. If the area is 58.5 square feet, find the length of the base and the height of the triangle.

Answer 1

The answer is the height h equals 9

Explanation:

`a = (1)/(2) bh = 58.5\\ b = h + 4`

`58.5 = ((h + 4)h)/(2) = \frac{ {h}^(2) + 4h}{2}`

`117 = {h}^(2) + 4h \\ {h}^(2) + 4h - 117 = 0`

`x1 = - 2 + u \\ x2 = - 2 - u\\ x1x2 = ( - 2 + u)( - 2 - u) = - 117`

`4 - {u}^(2) = - 117 \\ 4 + 117 = {u}^(2) \\ {u}^(2) = 121`

`\sqrt{ {u}^(2) } = + or - √(121) \\ u = + or - 11`

`x1 = - 2 + 11 = 9 \: or \\ x2 = - 2 - 11 = - 13`

since areas have to be positive -13 is incorrect therefore

`h = 9`

Check:

`58.5 = ((h + 4)h)/(2) = ((9 + 4)9)/(2) = \\ (13 * 9)/(2) = (117)/(2) = 58.5`