Question

Two adjacent sides of a parallelogram is in the ratio 5:6, Find the sides of the parallelogram
if its perimeter is 308 cm

​

Answer 1

Answer:

140and168

Step-by-step explanation:

5:6

=5x+6x=308

=11x=308

x=308/11

x=28

5x=5(28)=140

6x=6(28)=168

hence the two sides of a parallelogram is 140and168

Answer 2

Answer:

The sides of the parallelogram is 70 cm and 84 cm.

Step-by-step explanation:

$\Large\rm\blue{\underline{Given:-}}$

Adjacent sides = 5:6

Perimeter = 308 cm

$\Large\rm\blue{\underline{To\:Find:}}$

The sides of the parallelogram.

$\huge\rm\red{\underline{Explanation:}}$

Let the length of sides 1 and 3 be 5x and the length of side 2 and 4 be 6x.

$\large\rm\orange{\underline{According\:to\:question,}}$

Used Furmula:-

$\bigstar\boxed{ \red{Perimeter\:of\:Parallelogram=Sum\:of\:all\:sides}}$

$\implies\bf 5x + 5x + 6x + 6x = 308 \\ \implies\bf 22x = 308 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies\bf \: x = \dfrac{308}{22} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies\bf x = 14 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

We know that in a parallelogram, opposite sides are equal.

Therefore, The length of sides 1 and side 3 =

$\bf = 5x = 5(14) = 70$

Therefore, The length of sides 2 and 4 =

$\bf = 6x = 6(14) = 84$

Hence, The length of sides is 70 cm and 84 cm.

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$\Large\rm\red{\underline{Verification:}}$

We know now that perimeter of parallelogram is sum of all sides and also know that opposite side is always equal in parallelogram.

1st side = 70 cm

2nd side = 84 cm

3rd side = 70 cm

4th side = 84 cm

Perimeter = Sum of all side

Then,

70 + 84 + 70 + 84 = 308 cm

$\Large\rm\red{\underline{Hence\:Verified}}$

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$\Large\rm\red{\underline{Difination:}}$

1. A quadrangle with two pairs of parallel sides is called a parallelogram.

2. A quadrangle which has four right angles is called a rectangle.

3. A parallelogram that has two adjacent equal sides, is called a rhombus.