Question

Help me understand this problem

Answer 1

It ΔABC and ΔXYZ are similar, then the sides of the triangles are in proportion.

$\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}$

We have BC = 8, AC = 7, Y = 28, XZ = 49 and YZ = 56. Substitute:

$\dfrac{AB}{XY}=\dfrac{BC}{YZ}\to\dfrac{AB}{28}=\dfrac{8}{56}\qquad\text{cross multiply}\\\\56AB=(8)(28)\qquad\text{divide both sides by 56}\\\\AB=\dfrac{224}{56}\\\\\boxed{AB=4}$