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Use the area to find the lengths of the non-hypotenuse sides as one can be expressed in terms of the other giving one variable to be found.

Then use Pythagoras on them to find the hypotenuse.

That's how to do it, this is it being done:

Let the shortest side be x cm long. Then the other side is (x+1.5).

The area is:

13.5 = 1/2 x x x (x+1.5)

â‡’ 27 = x2 + 1.5x

â‡’ 2x2 + 3x - 54 = 0

â‡’ (2x - 9)(x + 6) = 0

â‡’ x = 4.5 or -6

As the length must be positive, x = 4.5, making the sides 4.5 cm and 6 cm

Using Pythagoras:

hypotenuse2 = 4.52 + 62

â‡’ hypotenuse = 7.5 cm

Q: How would you find the length of the hypotenuse of a right angle triangle when one side is 1.5 cm less than the other side and it has an area of 13.5 square cm?

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