Question

50 POINTS: Please help thank you so much!! (Image attached) The polygons are similar. Find the values of the variables.

I know from the answer key that the answers are x=
3 \sqrt{10}310​
and y=
2 \sqrt{10}210​
but I'm not sure how to get there...​

Answer 1

Answer and Step-by-step explanation:

These are right triangles, and the second triangle has two known sides. We can use the Pythagorean theorem to find y.

$A^2 + B^2 = C^2$ is Pythagorean theorem.

$3^2 + y^2 = 7^2\\\\\\9 + y^2 = 49\\\\\\y^2 = 40\\\\\\y = 2\sqrt{10}$

Now, we want to find x.

We know the triangles are similar.

4.5 divided by 3 is 1.5. This is the scale factor for the triangle.

If we multiply y by 1.5, we will get 5x.

$5x = 1.5(2\sqrt{10} )\\\\\\5x = 3\sqrt{10} \\\\\\Divide.5.on.both.sides.to.get.x.\\x = \frac{3\sqrt{10} }{5}$

Those are the answers and how to get them.

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