Question

The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base

Answer 1

Since the area of a triangle is in the form
area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus  x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12