Question

The Perimeter of a right angle Triangle is 12cm, if the hypotenuse is 5cm, how do you find the area and two sides of a triangle?

Answer 1

Let the two legs of the triangle be `x` and `y`.

Then `x + y + 5 = 12` and `x^2 +y^2 = 5^2`

`y = 7 - x`

Substituting:

`x^2 + (7 - x)^2 = 25`

`x^2 + 49 - 14x + x^2 = 25`

`2x^2 - 14x + 24 = 0`

`2(x^2 - 7x + 12) = 0`

`2(x - 3)(x - 4) = 0`

`x = 3 and 4`

The two legs measure `3` and `4` cm. The area is given by `A = (B xx H)/2`, where `B` and `H` are the two legs.

`A = (3 xx 4)/2`

`A = 6` square centimetres.

In summary:

The triangle has sides of `3, 4 and 5` centimetres. The area is of `12" cm"^2`

Hopefully this helps!