Question

In figure ∆ ABC is similar to ∆ DEC, AB = 20 AC= 48 BC: EC = 2:3, find DC.​

Answer 1

Explanation:

Given that ,

∆ ABC ~ ∆ DEC

• AB = 20
• AC = 48
• BC : CE = 2 : 3

Since they are similar triangles

The ratio of the corresponding sides are equal

⇛ AB / DE = BC / EC = AC / DC

⇛ AB / DE = AC / DC = 2/3

⇛ 20/DE = 48/DC = 2/3

On taking 48/DC = 2/3

On applying cross multiplication then

⇛ 2×DC = 48×3

⇛ DC = 48×3/2

⇛ DC = 24×3

⇛ DC = 72

and

On taking 20/DE = 2/3

On applying cross multiplication then

⇛ 2×DE = 3×20

⇛ DE = 3×20/2

⇛ DE = 3×10

⇛ DE = 30

Answer:

The value of DE = 30.

The value of DC for the given problem is 72.

Key Knowledge:

1. The two triangles are similar ,if
2. The corresponding sides are in the same ratio or in Proportion.
3. The corresponding angles are equal.