Answer:
x = y = 20
Explanation:
The two triangles shown are similar because one is simply an extension of othe other.
From this, we can use a similar side lengths formula specifically for triangles.
Notice that this represents the ratio of the whole side to the smaller side and says that this proportion is equal to the proportion for its adjacent side lengths. Cross mutiply the above equation to solve for y.
12(y+5) = 15y
12y + 60 = 15y
y = 20
Now we need to find the value of x. We have a side and hypotenuse's length of this large triangle, so we can use the pythagorean theorem to calculate the unknown side length.
(12 + 3)² + x² = (20 + 5)²
15² + x² = 25²
225 + x² = 625
x² = 400
x = ±20
The negative 20 doesn't make sense for this application so use the positive 20.
Therefore x = 20, y = 20.