Question

220% Find x and y. 11. 12. X у X 10 4 3 9 14. 13. 4 y 5 15 Х 2 2 у

Answer 1

Could you please provide an image with the actual question?

Which of the four triangles you need help with?

We are asked to find the segments identified with x and y in the following images:

so, we are going to be using the proportionality between similar triangles, since the three right angle triangles determined in each image are in fact similar triangles.

the proportion tells us that the hypotenuse of each right angle triangle is to the long leg as it is in each of the similar triangles.

In problem 13 we can then write:

using the larger triangle which has hypotenuse given by 15 + 4 = 19

19/y = y/15

this way using the proportion between sides of the larger triangle and of the medium size triangle.

we cross multiply to solve for y in the equation, and get:

19 * 15 = y^2

285 = y^2

we need now to use the square root property to solve for y as shown below:

`\begin{gathered} y^2=285 \\ y=\sqrt[]{285} \\ y\approx16.8819 \end{gathered}`

Now, that we know the value of y, we can solve for x using another proportion, or simply by using the Pythagoras theorem:

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