Question

In the figure, AB || DE. Find the length of CD

Answer 1

since both the triangles are similar in 1/2 ratio
CD=2.5 cm
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Answer 2

Answer:

According to the figure, length of CD is 2.5cm.

Step-by-step explanation:

According to the diagram if we write ΔABC is similar to ΔDCE, we get

⇒ ∠ACB = ∠DCE   [∵ Vertical Opposite Angles]

Now, ∠ABC must be equal to ∠CDE

i.e. ∠ABC = ∠CDE   [∵ It form Internal Alternate Angles]

which means,

ΔABC ~ ΔDCE    [ "~" means similar]

Now we have the ratio of

AB/DE = AC/CE = BC/CD

If we compare AB/DC and BC/CD we get,

⇒ AB/ED = BC/CD

⇒ CD = (BC × ED)/AB

⇒ CD = (5cm × 3cm)/6cm    [∵ BC = 5cm; ED = 3cm; AB = 6cm]

⇒ CD = (5/2)cm or CD = 2.5cm.

Hence the length of CD is 2.5cm.