Question

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

Answer 1

Answer:

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

Step-by-step 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.