# A triangle has an area of 77 square inches. How do you find the length of the base if the base is 3 inches more than the height?

Jan 8, 2016

Solve the quadratic equation to get $b = 14$

#### Explanation:

If the base of a triangle is $b$ and the height is $h$, the area $A = \frac{1}{2} b h$
In this example $h = b - 3$ and $A = 77$
$\therefore 77 = \frac{1}{2} b \left(b - 3\right)$
$154 = {b}^{2} - 3 b$
${b}^{2} - 3 b - 154 = 0$

$154 = 77 \cdot 2 = 7 \cdot 11 \cdot 2 = 11 \cdot 14$
$11 - 14 = - 3$ so these are the factors we need

$\left(b - 14\right) \left(b + 11\right) = 0$
$b$ cannot be equal to $- 11$ as we are dealing with a real entity (the triangle) so $b = 14$