Question

Sherry draws a triangle. The length of side AC is 8 inches. The length of side AB is 9 inches. She wants to draw a line XY that is parallel to BC. If she draws point X 2 inches from B, how far from C does she need to draw point Y do that XY || BC?

Answer 1

see the figure below to better understand the problem

we have that

If XY is parallel to BC

then

Triangle ABC is similar to triangle DBE

Remember that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.

I will assume that triangle ABC is a right triangle

so

AB^2+AC^2+BC^2

BC^2=9^2-8^2

BC^2=17

BC=√17

Applying proportion

DE/AC=BE/BC

substitute given values

DE/9=2/√17

DE=(2/√17)*9

DE=4.37

therefore

Point Y should be 4.37 inches from point C