Question

two adjacent sides of a parallelogram are in the ratio 3:8 and its perimeter is 110 cm find the sides of parallelogram

Answer 1

let first side (a) be 3x and second side (b) be 8x
we know that perimeter of parallelogram = 2(a+b)
then 2( 3x + 8x )= 110
= 2×11x= 110
= 11x = 110÷2
11x= 55
x= 55÷11
x=5

then 1st side= 3x=3×5 =15
2nd side= 8x=8×5=40

Answer 2

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• All the sides of parallelogram = 15cm, 40cm, 15cm, 40cm

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• Two adjacent sides of a parallelogram are in the ratio 3:8 and its perimeter is 110 cm.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• All the sides of parallelogram = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

$\sf\underline{\pink{\:\:\: Diagram:-\:\:\:}}$

$\setlength{ \unitlength}{20} \begin{picture}(3,5) \put(2,2){ \line(1,0){4}}\put(2,2){ \line(1,1){3}}\put(6,2){ \line(1,1){3}} \put(5,5){ \line(1,0){4}} \put(2,1.5 ){ \tt A } \put(6, 1.5){ \tt B } \put(5,5.2){ \tt D } \put(9.3, 5){ \tt C } \put(4, 1.5){ \tt 8x } \put(7.5,3 ){ \tt 3x } \put(3, 3.5){ \tt 3x } \put(7,5.2 ){ \tt 8x } \\ \put(8,1)}}\end{picture}$

$\rule{200}{2}$

$\textbf {Let the constant ratio = x}$

$\textbf {Let the first adjacent side be 3x}$

$\textbf {And Second adjacent side be 8x}$

• Perimeter = 110 Cm [Given]

$\dashrightarrow \sf {2( sum\: of \:adjacent \:sides) = 110\:Cm}$

$\dashrightarrow \sf {2( 3x + 8x) = 110}$

$\dashrightarrow \sf {2 (11x) = 110}$

$\dashrightarrow \sf {22x = 110}$

$\dashrightarrow \sf {x = \dfrac{\cancel{110}}{\cancel{22}} }$

$\dashrightarrow \sf { x = 5 }$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

First Adjacent side = 3x

First Adjacent side = 3 × 5

First Adjacent side = 15cm

$\sf\underline{\green{\:\:\: And:-\:\:\:}}$

Second Adjacent side = 8x

Second Adjacent side = 8 × 5

Second Adjacent side = 40cm

$\sf\underline{\red{\:\:\: Since:-\:\:\:}}$

• We know opposite sides of parallelogram are equal.

$\sf\underline{\red{\:\:\: Then:-\:\:\:}}$

• Other two sides of parallelogram are 15cm and 40cm.

$\sf\underline{\red{\:\:\: Thus:-\:\:\:}}$

• All the sides of parallelogram are 15cm, 40cm, 15cm, 40cm.

$\rule{200}{2}$