Question

Given ABC find the values of x and y. In your final answer, include all of your calculations.

Answer 1

So with this, we will be using proportions. To solve for x, our proportion will be
`(x)/(6) =(6)/(x-9)`

Firstly, cross-multiply:
`x^2-9x=36`

Next, subtract 36 on both sides:
`x^2-9x-36=0`

Next, replace -9x with 3x-12x
`x^2+3x-12x-36=0`

Next, factor x^2+3x and -12x-36 separately:
`x(x+3)-12(x+3)=0` . After, rewrite it as
`(x-12)(x+3)=0`

Next, solve for x separately in the two parentheses:

`x-12=0\\ x=12`

`x+3=0\\ x=-3`

Since we can't have a negative length, x = 12.

To solve for y, our proportion will be
`(y)/(9) =(12)/(y)`

Firstly, cross-multiply:
`y^2=108`

Next, just square root each side, and your answer will be (rounded to hundredths)
`y=10.39`

In short, x = 12 and y = 10.39.