. Ratio of length of a pair of adjacent sides of a parallelogram PQRS is 3:5 and its perimeter is 160 cm. Find the length of its each side.
Answers
Answer :
The length of sides of the parallelogram are 30cm , 50cm , 30cm ,50cm.
Step-by-step Explanation :
( Please see the attached document for diagram)
Given : ABCD is a parallelogram
AB : BC = 3 : 5
Perimeter of parallelogram ABCD = 160 cm.
To find : Length of its each side = ?
We know that,
AB = CD and BC = AD ------- (1) (Opposite sides of a parallelogram are congruent)
AB : BC = 3:5 ------- (Given)
Let the common multiple be x.
AB = 3x and BC = 5x -------- (2)
CD = 3x and AD = 5x ----------- (3) [ From (1) and (2) ]
Perimeter of parallelogram ABCD = AB + BC + CD + AD
Substituting the value in above formula we get,
160 = 3x + 5x + 3x + 5x
160 = 16x
x = 160/16
x = 10 cm
AB = 3x = 3 x 10 = 30 cm
BC = 5x = 5 × 10 = 50 cm
Hence The length of sides of the parallelogram are 30cm , 50cm , 30cm ,50cm .
