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

Answer:

h = 28 inches

Step-by-step explanation:

Let the base of the triangle is b.

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

h = 4b-4

The area of the triangle is 112 inch².

The formula for the area of a triangle is given by :

$A=\dfrac{1}{2}bh\\\\112=\dfrac{1}{2}\times b\times (4b-4)$

It is a quadratic equation, whose solution is as follows :

b = -7 and b = 8 inches

Height, h = 4(8)-4

= 32-4

= 28 inches

Hence, the height of the triangle is 28inches.