Math CentralQuandaries & Queries


Question from sharul, a student:

find the dimension of isosceles triangle of largest area with perimeter 12cm

Hi Sharul,

I drew an isosceles triangle, let its base be 2b cm long and then the other two sides must have lengths 6 - b cm in order that the perimeter is 12 cm.


In the diagram D is the midpoint of the base so h is the height of the triangle. Since triangle ADC is a right triangle you can use Pythagoras' Theorem to write h in terms of b. Write the area of the triangle as

A = 1/2 b h

and thus A is a function of b alone. Use your knowledge of calculus to maximize this expression.


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