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

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=(1)/(2)xh`

Substitute h=12-x into the equation

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