How do you find the area of an isosceles right angle triangle with a perimeter of 40 units?
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:
the perimeter is 40
(3) Find the area
take out common factors
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