If you know the perimeter of a right angled triangle, what can you say about the area?
If this right-angled triangle has a perimeter of 12 units, it is possible to show that the area is 36−6c square units.
Can you find a way to prove it?
Once you’ve had a chance to think about it, click below to see a possible way to solve the problem, where the steps have been muddled up.
Can you put them in the correct order?
d) So 2ab=144−24c
e) Area of the triangle =ab2
f) By Pythagoras’ Theorem, a2+b2=c2
h) Dividing by 2: ab=72−12c
Can you adapt your method, or the method above, to prove that when the perimeter is 30 units, the area is 225−15c square units?
Can you find a general expression for the area of a right angled triangle with hypotenuse c and perimeter p?
Age 14 to 16