Question

The height of the triangle is 4 inches less than four times its

base. The area of the triangle is 112 in2. What is the height of
the triangle?

Answer 1

Let base = b

Given height, h is 4inches less than base. So h = b - 4

`Area = (1)/(2) * base * height\\\\112 = (1)/(2) b *(b-4)\\224 = b(b -4)\\b^2 - 4b -224 = 0\\\\b= (4 \pm √(16 - (4* -224)) )/(2) \\\\\\b= (4 + √(16 +896 ) )/(2) , b= (4 - √(16 +896) )/(2) \\\\\\b = 17.099 , -13.099`

Since length can't be negative, we take b = 17.099inches

Height ,h = b - 4 = 13.099 inches ≈ 13.1 inches