# The base and height of a triangle have the same length. If the length of the base is increased by 4 cm. the area becomes 96 sq cm. Find the length of the base of the original triangle.

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

Since base = height of original triangle, we can call each "x".

So, this means that in order to find area of a triangle, we use the formula:

`A = 1/2 bh`

So, the height of the triangle is still "x" as that did not increase.  Which makes the base "x + 4" as it increased by 4.   The area of new triangle is 96, so:

`96 = 1/2 x(x+4)` To solve I will multiply both sides by 2, to get rid of `1/2.`

This gives:  `192 = x(x+4)` .  Use distributive proeprty to give:

`x^2 + 4x = 192` .  This is a quadratic, so we will set equal to zero and factor.

`x^2 + 4x - 192 = 0` Factor.

`(x + 16)(x - 12) = 0` Therefore x = -16 or x = 12.  Since we are dealing with a triangle and can't have negative lengths,  `x = 12.`

Since x represents both base and height of original triangle.  The base has lenght of 12.