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

Answer:

The answer is the height h equals 9

Step-by-step explanation:

$a = \frac{1}{2} bh = 58.5\\ b = h + 4$

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

$117 = {h}^{2} + 4h \\ {h}^{2} + 4h - 117 = 0$

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

$4 - {u}^{2} = - 117 \\ 4 + 117 = {u}^{2} \\ {u}^{2} = 121$

$\sqrt{ {u}^{2} } = + or - \sqrt{121} \\ u = + or - 11$

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

since areas have to be positive -13 is incorrect therefore

$h = 9$

Check:

$58.5 = \frac{(h + 4)h}{2} = \frac{(9 + 4)9}{2} = \\ \frac{13 \times 9}{2} = \frac{117}{2} = 58.5$