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Nata [24]
3 years ago
5

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 t

he sides of the triangle
Mathematics
1 answer:
Harrizon [31]3 years ago
7 0

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

<u>Shortest Leg = 36 - 9 = 27</u>

<u>Longest Leg = 36</u>

<u>Hypotenuse = 45</u>

<u></u>

<u>#teamtrees #WAP (Water And Plant)</u>

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