Question

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Question: The length of one leg of a right triangle is 3 feet shorter than the other leg. The length of the hypotenuse is 3 feet longer than the longer leg. What is the length of the shortest leg of the triangle?

Answer 1

9

Explanation:

→You can use the Pythagorean Theorem to solve this, by plugging in the numbers, like so:

`a^2+b^2=c^2\\x^2+(x-3)^2=(x+3)^2`

`x^2+x^2-6x+9=x^2+6x+9`

→Subtract
`x^2-6x+9` from both sides:

`x^2 = 12x`

→Subtract 12x from both sides:

`x^2 -12x=0`

→Factor out x:

`x(x-12)=0`

→Separate, set = to 0, and solve:

`x = 0\\x -12=0` → Add 12 to both sides:
`x = 12`

→So we have 0 and 12, as our answers. However, we cannot have 0 as a side length, since this would not be possible.

→All we need to do is take 12, and plug it into the equation for the shortest leg.

`x - 3=?\\12-3=9`