# How do you find the area of an isosceles right angle triangle with a perimeter of 40 units?

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An isosceles triangle has two of its sides the same length.

This triangle is also a right angled triangle so Pythagoras's Theorem holds.

**(1) find the hypotenuse**

call the equal lengths

then we have by Pythagoras

so the sides are:

**(2) Find #x#**

the perimeter is 40

**(3) Find the area**

take out common factors

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Let the two equal sides of the triangle be

The hypotenuse is

By Pythagoras: The square on the hypotenuse is equal to the sum of the squares on the other two sides.

The equal sides of the right-angled isosceles triangle are also the base and height. Use

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