Question

The base of a triangle exceeds the height by 7 feet. If the area is 114 square feet, find the length of the base and the height of
the triangle

Answer 1

Answer:

Height of the triangle = 12 feet

Base of the triangle = 19 feet

Step-by-step explanation:

Let the height of the triangle be x feet

-> Base of the triangle = (x + 7) feet

$A(\triangle)= 114\: ft^2$

$\because A(\triangle)=\frac{1}{2}(base)(height)$

$\implies 114=\frac{1}{2}(x+7)(x)$

$\implies 114\times 2= x^2+7x$

$\implies 228= x^2+7x$

$\implies x^2+7x-228=0$

$\implies x^2+19x-12x-228=0$

$\implies x(x+19)-12(x+19)=0$

$\implies (x+19)(x-12)=0$

$\implies (x+19)=0,\:\:(x-12)=0$

$\implies x =-19,\:\:x=12$

x represents the height of the triangle.

-> x can not take negative value.

$\implies x\neq -19$

$\implies x = 12$

$\implies x +7= 12+7=19$

Thus,

Height of the triangle = 12 feet

Base of the triangle = 19 feet