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=(bh)/(2)`. Or

`A(h)=((26-h)h)/(2)`.

When the area is maximum,
`(dA)/(dh) =0`.

or,

`(d((26-h)h)/(2) )/(dh) =0`.

`(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`