the ratio of the sides of a parallelogram is 3: 5 and the perimeter is 48cm find the sides
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the ratio of the sides of a parallelogram is 3: 5 and the perimeter is 48cm find the sides
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Answer:
Let the sides be 3x and 5x respectively,
Since, perimeter of parallelogram = 2 ( l+b)
ATQ,
2 ( 3x + 5x) = 48
2 ( 8x) = 48
8x = 24
x = 24/8
x = 3
So, The sides are, 3x = 9cm and 5x = 15cm
Hope This helps ☺️
Given :-
To Find :-
Formula Used :-
[tex] \bigstar \: \boxed{ \bf Perimeter_{(Parallelogram)} \: = \: 2(l+b)} \: \bigstar[/tex]
Solution :-
Given that,
[tex]⇝\;[/tex] The perimeter of a parallelogram is 48cm
[tex]⇝\;[/tex]The ratio of the sides of a parallelogram is 3 : 5
Let,
[tex]⟶\;[/tex] 3 : 5 = 3x and 5x
According to the question by using formula we get,
[tex]\sf \implies \: Perimeter \: = \: 2(l+b)[/tex]
[tex]\sf \implies \: 48 \: = \: 2(3x+5x)[/tex]
[tex]\sf \implies \: 48 \: = \: 2(8x)[/tex]
[tex]\sf \implies \: 48 \: = \: 16x[/tex]
[tex] \displaystyle\sf \implies \: \frac{3}{1} \: = \: x[/tex]
[tex] \displaystyle\sf \implies \: 3 \: = \: x[/tex]
[tex] \displaystyle\bf \implies \: \underline{x \: = \: 3}[/tex]
Hence,
The sides of a parallelogram :
[tex] \longmapsto \: \: \sf3x = 3(3) = \bf 9cm[/tex]
[tex] \longmapsto \: \: \sf5x = 5(3) = \bf 15cm[/tex]
Finally,
[tex] \boxed{ \bf \therefore The \: sides \: of \: a \: parallelogram \: are \: 9cm \: and \: 15cm} \\ \\ [/tex]