Question

Question #2b1ec

Answer 1

The smaller leg is `8.83095 cm` long.

Explanation:

Let the shorter leg of the right triangle have a length of value `x`.

The longer leg would then have a length of `x+3`.

The hypotenuse would then have a length of `x+6.`

If we consider the Pythagorean Theorem `a^2 +b^2 = c^2`, and input
`a` as the shorter leg, `x`,
`b` as the longer leg, `x+3`, and
`c` as the hypotenuse `x+6`, you will have:

`(x)^2 + (x+3)^2 = (x+6)^2`.

Expanded, this gives

`x^2 + x^2 + 6x+ 9 = x^2+12x + 36`. When combined and when everything is moved over to the left, it is:

`x^2 - 6x - 25 = 0`.

If you use the quadratic formula or you factor this on a calculator, you will get

`x = 8.83095 or x = -2.83095`

Since distance can't be negative, the answer is`x= 8.83095 cm.`