Question

Find x and y for this triangle

Answer 1

x = 1.25

x = 1.75

Explanation:

I marked the points of this triangle in the attached image so it's easier to explain.

ΔABC is similar to ΔADE, and all pairs of corresponding sides are proportional as a result.

`(DE)/(BC)=(AD)/(AB)=(AE)/(AC)`

The length of the sides BC and DE is given, so I'll start with that and set it equal to the proportion between AB and AD.

`(DE)/(BC)=(AD)/(AB)\\\\(10)/(8)=(x+5)/(5)\\\\10*5=(x+5)*8\\50=8x+40\\10=8x\\x=1.25`

Now, you can do the exact same thing for y:

`(DE)/(BC)=(AE)/(AC)\\\\(10)/(8)=(y+7)/(7)\\\\10*7=(y+7)*8\\70=8y+56\\14=8y\\y=1.75`