Atriangle has an area of 77 square inches. find the length of the base if the base is 3 inches greater than the height

Answer:

Length of base of the triangle is 14 inches.

Explanation;

Given:

Area of A triangle = 77 square inches

The base is 3 inches greater than the height

To find:

The length of the base of the triangle=?

Solution:

Let assume height of the triangle = x  

As base is 3 inches greater than the height, so base of the triangle = x + 3

=>

And as given that area of triangle = 77 , we get

=>

=> = 0

= 0

Solving above equation using quadratic formula.

General form of quadratic equation is  

And quadratic formula for getting roots of quadratic equation is  

In our case b = 3 , a = 1 and c = -154

Calculating roots of the equation we get

  ,  

x= 11 ,  x= -14

Since height cannot be negative, ignoring negative value we get

x= 11  

Base of the triangle = x + 3 = 11 + 3 = 14

Hence length of base of the triangle is 14 inches.