Question

In the figure (1) given below, AB || DE, AC = 3 cm, CE = 7.5 cm and BD = 14 cm. calculate CB and DC.​

Answer 1

Step-by-step explanation:

From the question it is given that,

AB∥DE

AC=3cm

CE=7.5cm

BD=14cm

From the figure,

∠ACB=∠DCE [because vertically opposite angles]

∠BAC=∠CED [alternate angles]

Then, △ABC∼△CDE

So, AC/CE=BC/CD

3/7.5=BC/CD

By cross multiplication we get,

7.5BC=3CD

Let us assume BC=x and CD=14−x

7.5×x=3×(14−x)

7.5x=42−3x

7.5x+3x=42

10.5x=42

x=42/10.5

x=4

Therefore, BC=x=4cm

CD=14−x

=14−4

=10cm