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
[tex]A(\triangle)= 114\: ft^2[/tex]
[tex]\because A(\triangle)=\frac{1}{2}(base)(height) [/tex]
[tex]\implies 114=\frac{1}{2}(x+7)(x) [/tex]
[tex]\implies 114\times 2= x^2+7x[/tex]
[tex]\implies 228= x^2+7x[/tex]
[tex]\implies x^2+7x-228=0[/tex]
[tex]\implies x^2+19x-12x-228=0[/tex]
[tex]\implies x(x+19)-12(x+19)=0[/tex]
[tex]\implies (x+19)(x-12)=0[/tex]
[tex]\implies (x+19)=0,\:\:(x-12)=0[/tex]
[tex]\implies x =-19,\:\:x=12[/tex]
x represents the height of the triangle.
-> x can not take negative value.
[tex]\implies x\neq -19[/tex]
[tex]\implies x = 12[/tex]
[tex]\implies x +7= 12+7=19[/tex]
Thus,
Height of the triangle = 12 feet
Base of the triangle = 19 feet
