Question

Please help me find x and y

Answer 1

Given:

(the photo)

Asked:

Find the values of x and y.

Step-by-step explanation:

There are three right triangles in the figure. We can use the first triangle on the upper left corner to find the value of y by applying the Pythagorean Theorem.

`{y}^(2) + {5}^(2) = {10}^(2)`

`{y}^(2) + 25 = 100 \\ {y}^(2) = 75 \\ y = 5 √(3)`

Next, we know that the altitude to the hypotenuse is the geometric mean of the segments formed in the hypotenuse. So, we get the following equation to solve for

x:

`5x = y2`

Substituting the value of y we got earlier, we have:

`5x = {y}^(2)`

`5x = 75`

`x = 15`

Answers:

`x = 15`

`y = 5 √(3)`