Question

This figure shows two triangles, A B C and F E D. Side D F measures 6.5 units. Side D E measures 5 units. Segment X Y is drawn parallel to A C from point X on side A B to point Y on side B C. Segment B Y measures 3 units.



















This figure shows two triangles, A B C and F E D. Side D F measures 6.5 units. Side D E measures 5 units. Segment X Y is drawn parallel to A C from point X on side A B to point Y on side B C. Segment B Y measures 3 units.
Note: Figure not drawn to scale.
Triangles

and

shown are congruent. Line segment


is parallel to


, and the length of


. What is the length of


?

Answer 1

Since triangles A B C and F E D are congruent, the corresponding sides are proportional.

The length of AC is 5 units, which corresponds to the length of ED which is also 5 units.

Since XY is parallel to AC, triangle AXY is similar to triangle CBY. This means that the ratios of corresponding sides are equal.

Therefore, (AC/BC) = (AX/CY)

Substitute the given values: 5/(5 + BC) = 3/CY

Solving for CY, we get: CY = (5/3) * (5 + BC)

BC + 5 = 3CY/5

BC + 5 = 3(5 + BC)/5

BC + 5 = 15/5 + 3BC/5

5BC + 25 = 15 + 3BC

2BC = -10

BC = -5

Therefore, the length of BC is 5 units.