Question

Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?

Answer 1

Answer:

Option D. AC= 10 cm and CE= 5 cm

Step-by-step explanation:

From the given figure two triangles ΔABC and ΔADE are similar and two lines BC║DE.

From these similar triangles we know

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

$\frac{8}{12}=\frac{BC}{9}=\frac{AC}{AE}$

Therefore $\frac{AC}{AE}=\frac{8}{12}=\frac{2}{3}$

Or AC=$\frac{2}{3}AE$

Now from pythagoras theorem

AE = √(AD²+ED²) = √(12²+9²) = √(144+81) =√225 = 15 cm

Since we know side AC = $\frac{2}{3}AE$

                                        = $\frac{2}{3}\times 15$

                                        = 10 cm

Therefore AC = 10 cm and AE = 15cm and CE = (15-10) = 5 cm