The base of a triangle is 10 inches more than 3 times the height. If the area of the triangle is 16 square inches, find the base and the height

llm

Answered on Tue Mar 22 2022

Let the height be x

Then, base of the triangle will be 3x + 10

Area of triangle = 16 square inches

Formula :

Area of triangle = 1/2 × b × h

Putting values, we get

16 = 1/2 × (3x+10) × x

32 = 3x² + 10x

3x² + 10x - 32 =0

3x² + 16x - 6x - 32 =0

x(3x-16) - 2(3x + 16) =0

(x-2) (3x-16) =0

So, x -2 =0

x =2

And, 3x +16 =0

3x = -16

x = -16/3

Height cannot be negative. So, height of the triangle is 2 inches

Then, base = 3(2) + 10

Base = 6 + 10

Base = 16 inches.

Thus, height and base of the triangle are 2 inches and 16 inches respectively.