Question

The sum of the base and height of a triangle is 12 cm. What is the largest area that the triangle can have? (see figure)

Answer 1

SOLUTION

It is given that the sum of the base and is 12

It follows:

$\begin{gathered} x+h=12 \\ h=12-x \end{gathered}$

The area of the triangle is:

$A=\frac{1}{2}xh$

Substitute h=12-x into the equation

$\begin{gathered} A=\frac{1}{2}x(x-12) \\ A=\frac{1}{2}x^2-6x \end{gathered}$