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:

       |\

       |   \

       |     \

       |        \

       |           \

       |              \   9 + x

x - 9 |                 \

       |                    \

       |                      \

       |                        \

       |                          \

       |_____________\

                    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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