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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.
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