Question

Find the side lengths of the triangle in this picture.​

Answer 1

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

Explanation:

According to the statement, we have the following information about the lengths of the right triangle:

Hypotenuse

`3\cdot x + 14`

Long leg

`3\cdot x + 13`

Short leg

`x`

By the Pythagoric Theorem, we have the following expression:

`(3\cdot x + 14)^(2) = x^(2) + (3\cdot x + 13)^(2)` (1)

`9\cdot x^(2)+84\cdot x + 196 = x^(2) + 9\cdot x^(2) + 78\cdot x + 169`

`9\cdot x^(2) + 84\cdot x + 196 = 10\cdot x^(2) + 78\cdot x +169`

`x^(2) -6\cdot x -27 = 0`

`(x-9)\cdot (x+3) = 0`

As length is a positive variable by nature, then the only possible solution is
`x = 9`. Lastly, the side lengths of the right triangle are:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.