Question

The base of a triangle is 3 inches more than 3 times the height. If the area is 30 square inches, find the base and the height.Base:_ inchesHeight: _inches

Answer 1

Base : 15 inches

Height : 4 inches

EXPLANATION :

Recall the area formula of a triangle :

`A=(1)/(2)bh`

The area of the triangle is 30 in^2

The base is 3 inches more than 3 times the height so :

`b=3h+3`

Using the formula above :

`\begin{gathered} A=(1)/(2)bh \\ 30=(1)/(2)(3h+3)(h) \\ 60=3h^2+3h \\ 0=3h^2+3h-60 \\ 3h^2+3h-60=0 \\ \text{ Divide both sides by 3 :} \\ h^2+h-20=0 \\ \text{ Factor completely :} \\ (h+5)(h-4)=0 \end{gathered}`

Equate the factors to 0.

h + 5 = 0

h = -5

h - 4 = 0

h = 4

Since there's no negative dimension, we will only consider h = 4

Solve for the base :

`\begin{gathered} b=3h+3 \\ b=3(4)+3 \\ b=15 \end{gathered}`