Question

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Answer 1

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Answer 2

Explanation:

Given :-

∆ ABC ~ ∆ DEC

AB = 20

AC = 48

BC : CE = 2 : 3

To find :-

Find the value of DC ?

Solution :-

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

Used formulae:-

The two triangles are similar ,if

• The corresponding sides are in the same ratio or in Proportion.

• The corresponding angles are equal.