Question

A right triangle with a long leg (x+7) and a short leg with (x) and the hypothenuse is 13

Answer 1

Area is 30cm^2 if thats what your asking

Explanation:

Answer 2

X = 5

Explanation:

You need to use the Pythagorean theory to solve this question.

`{13}^(2) = {x}^(2) + {(x + 7)}^(2)`

`169 = {x}^(2) + ( {x}^(2) + 14x + 49)`

`169 = 2 {x}^(2) + 14x + 49`

`0 = 2 {x}^(2) + 14x + 49 - 169`

`0 = 2 {x}^(2) + 14x - 120`

Now simply the equation by dividing everything by 2.

`0 = {x}^(2) + 7x - 60`

`0 = (x - 5)(x + 12)`

Now, you can find the possible solutions by setting each bracket to 0.

`0 = x - 5`

`5 = x`

OR

`0 = x + 12`

`- 12 = x`

However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.