Question

Find x and y for this triangle

Answer 1

Answer:

x = 1.25

x = 1.75

Step-by-step 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.

$\frac{DE}{BC}=\frac{AD}{AB}=\frac{AE}{AC}$

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.

$\frac{DE}{BC}=\frac{AD}{AB}\\\\\frac{10}{8}=\frac{x+5}{5}\\\\10\times5=(x+5)\times8\\50=8x+40\\10=8x\\x=1.25$

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

$\frac{DE}{BC}=\frac{AE}{AC}\\\\\frac{10}{8}=\frac{y+7}{7}\\\\10\times7=(y+7)\times8\\70=8y+56\\14=8y\\y=1.75$