The base of a triangle is 2 inches more than 2 times the height. If the area is 6 square inches, find the base and the height.

Question

Base: ___in.

Height: ___in.

Answer 1

Let h be the height of the triangle.

 

The formula for area of a triangle is given by:

 

Area = 1/2 * base * perpendicular height

 

Base of the triangle in terms of h

 

b = 2h + 2

 

6 = 1/2 * 2(h+1) * h

 

h^2 + h - 6 = 0

 

( h + 3 ) ( h - 2 ) = 0

Discard the negative value for h and use the positive one.

 

h = 2

 

A = 1/2 * 6 * 2

 

= 6 inches.

 

The height of the triangle is 2 in. , base is 6 in.