Question

The shorter leg of a right triangle is 9 ft shorter than the longer leg. The hypotenuse is 9 ft longer than the long leg. Find the sides of the triangle

Answer 1

Answer and Step-by-step explanation:

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| \ 9 + x

x - 9 | \

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|_____________\

x

That is your triangle.

Now, since its a right triangle, we can use the Pythagorean theorem to solve for x.

The equation for the Pythagorean theorem is this:
`A^(2) + B^(2) = C^(2)`

So we plug in the values.

`(x^(2) ) + (x-9)^(2) = (x + 9)^(2)`

We solve for x.

`x^(2) + x^(2) -18x + 81 = x^(2) + 18x + 81`

Get everything to the left side of the equation. (x^2 + x^2 = 2x^2, - x^2 = x^2;

-18x - 18x = -36x; 81 - 81 = 0)

`x^(2) -36x = 0`

Add 36x to both sides, then divide by x.

`x^(2) = 36x\\\\x = 36`

Shortest Leg = 36 - 9 = 27

Longest Leg = 36

Hypotenuse = 45

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