Question

The sum of the base and the height of a triangle is 2626 cm. find the dimensions for which the area is a maximum.

Answer 1

Let the height of the triangle be $h$ and the base be $b$.

Given that $h+b=26$ and the area of the triangle is $A=\frac{bh}{2}$. Or

$A(h)=\frac{(26-h)h}{2}$.

When the area is maximum, $\frac{dA}{dh} =0$.

or,

$\frac{d\frac{(26-h)h}{2} }{dh} =0$.

$\frac{d(26-h)h }{dh} =0$

$2h-26=0$

$h=13$

The dimensions of the triangle with maximum area is

$h=13 cm, b=13 cm$