Question

a triangle has an area of 77 square inches. Find the length of the base if the base is 3 inches greater than the height

Answer 1

Length of base of the triangle is 14 inches.

Step-by-step 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

`\text{{Area of triangle}} = (1)/(2)* height* base`=>
`Area of triangle = (1)/(2)* x *(x+3)`

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

`(1)/(2)* x*(x+3)=77`

=>
`x^2 + 3x = 77 * 2`

=>
`x^2 + 3x-154` = 0

`x^2 + 3x-154` = 0

Solving above equation using quadratic formula.

General form of quadratic equation is

`ax^2 +bx +c = 0`

And quadratic formula for getting roots of quadratic equation is

`x=\frac{-b\pm√((b^2-4ac))}2a`

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

Calculating roots of the equation we get

`x=(-(3)\pm√((3^2-4(1)( -154) )))/((2* 1))`

`x=(-(3)\pm√((9+616)))/((2*1))`

`x=(-3\pm√(625))/(2)`

`x=(-(3)\pm25)/(2)`

`x=((-3+25))/(2)` ,
`x=((-3-25))/(2)`

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.