Question

Plz help!! :( simplify answers & round to nearest tenth as needed

Answer 1

`1 + √(14)`

Explanation:

Using pythagorean theorem, x and x+6 are the legs, and x+7 is the hypotenuse.

You can express this as an equation.

`x^2 + (x+6)^2 = (x+7)^2`

Expanding, this is
`x^2+x^2+12x+36 = x^2+14x+49`

Grouping up, this is
`2x^2+12x+36 = x^2+14x+49`

Rearranging, this is
`x^2-2x-13 = 0`

Now, we can use the quadratic formula to solve.

`(-(-2) \pm √((-2)^2-4\cdot1\cdot(-13))/(2\cdot1)` =
`-1 \pm √(14)`. Since we need x to be positive (due to it being a side length), our answer is
`1 + √(14)`, because it is the positive option