16.△ABC is similar to △DEC, AB = 20 AC= 48 BC : EC = 2 : 3, find DC.
(1 Point)
32
72
Answers
Answer:
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Step-by-step explanation:
Given :-
∆ABC ~ ∆ DEC
AB = 20 units
AC = 48 units
BC :EC = 2:3
To find :-
Find the length of DC?
Solution:-
Given that
∆ABC ~ ∆ DEC
We know that
If two triangles are said to be similar ,
If the corresponding angles are equal.
If he Corresponding sides are in the same ratio.
=> AB/DE = BC/EC = AC/DC ------(1)
Given that
AB = 20 units
AC = 48 units
BC :EC = 2:3
=> BC/EC = 2/3
On Substituting these values in (1) then
=> 20/DE = 2/3 = 48/DC
On taking 20/DE = 2/3
On applying cross multiplication then
=> DE×2 = 20×3
=> DE = 20×3/2
=> DE = 10×3
=> DE = 30 units
On taking 2/3 = 48/DC
=> (2/3)×DC = 48
=>DC = 48×(3/2)
=>DC = 24×3
=> DC = 72 units
or
20/30 = 48/DC
On applying cross multiplication then
=> DC×20 = 30×48
=> DC = 30×48/20
=> DC = 3×24
=> DC = 72 units
Answer:-
→ The length of DC for the given problem is 72 units