What is the length of the hypotenuse of a right angle triangle when its area is 24 square cm and its perimeter is 24 cm giving clear details of your work?

Area = 1/2*base*height =24 cm2

Multiply both sides by 2: base*height = 48

Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

The only above numbers that will satisfy the criteria for the area and perimeter of the triangle are 6 and 8 because:

Area = 1/2*6*8 = 24 cm2

Perimeter = 6+8+10 = 24 cm

Therefore the length of the hypotenuse is 10 cm because it's the longest side.

Check using Pythagoras' Theorem:

62+82 = 100 and the square root of this is 10