Login/Sign Up
Home » In the figure given below, AB || DE, AC = 3 cm, CE = 7.5 cm and BD = 14 cm. Calculate CB and DC.
In the figure given below, AB || DE, AC = 3 cm, CE = 7.5 cm and BD = 14 cm. Calculate CB and DC.
CBSE | Class 10 | maths | Maths | ML Aggarwal | Similarity
In the figure given below, AB || DE, AC = 3 cm, CE = 7.5 cm and BD = 14 cm. Calculate CB and DC.

Solution:-

From the question it is given that,

AB||DE

AC = 3 cm

CE = 7.5 cm

BD = 14 cm

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 = 4 cm

CD = 14 – x

= 14 – 4

= 10 cm

i

More Material