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

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

$\text{{Area of triangle}} = \frac{1}{2}\times height\times base$=> $Area of triangle = \frac{1}{2}\times x \times(x+3)$

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

$\frac{1}{2}\times x\times(x+3)=77$

=> $x^2 + 3x = 77 \times 2$

=> $x^2 + 3x-154$ = 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  

$x=\frac{-b\pm\sqrt{(b^2-4ac)}}2a$

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

Calculating roots of the equation we get

$x=\frac{-(3)\pm\sqrt{(3^2-4(1)( -154) )}}{(2\times 1)}$

$x=\frac{-(3)\pm\sqrt{(9+616)}}{(2\times1)}$

$x=\frac{-3\pm\sqrt{625}}{2}$

$x=\frac{-(3)\pm25}{2}$

$x=\frac{(-3+25)}{2}$   ,  $x=\frac{(-3-25)}{2}$

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.