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

The sum of the base and the height of a triangle

allenlog000

13.03.2022

Let the height of the triangle be and the base be .

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

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trinigal83

24.05.2022

-2, -1

Step-by-step explanation:

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