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Ilia_Sergeevich [38]
3 years ago
12

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

Mathematics
1 answer:
kow [346]3 years ago
5 0

So with this, we will be using proportions. To solve for x, our proportion will be \frac{x}{6} =\frac{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 \frac{y}{9} =\frac{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.

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