line DE is parallel to line CB
Find the values of x and y

(see image below)

Please help me.
Thanks a bunch

Question

line DE is parallel to line CB
Find the values of x and y

(see image below)

Please help me.
Thanks a bunch

anonymous · Answer

attachment

mani_jha · Answer

Triangle ADE is similar to Triangle ABC. So
$$AD/AC=AE/AB=DE/BC$$

anonymous · Answer

ok.... what's the formula then?

anonymous · Answer

please help me :)

directrix · Answer

Let me think.

mani_jha · Answer

$$5/9=6/(6+x) x=4.8$$

directrix · Answer

If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, then it divides them proportionally.

So,

5 is to 4 as 6 is to x. and..

directrix · Answer

5/4 = 6/x

Using cross multiplication (Means-Extremes Property),

then 5x = 6*4

5x = 24

x = 24/5

I leave answers in reduced improper fractions. You may prefer mixed numbers.

anonymous · Answer

ok.. got it
thanks

directrix · Answer

We don't have y yet, and I think we don't have sufficient given information to get it.

Now, for y.

Triangle ADE is similar to triangle ACB by SAS Similarity Theorem

So, DE is to BC as AD is to AC.

DE/y = 5 / 9

We have a linear equation with two unknowns.