Question

The ratio of sides of a parallelogram is as 3:5and the perimeter is 48cm .find the sides of parallelogram

Answer 1

GIVEN:

• The ratio of sides of a parallelogram is as 3:5
• The perimeter of parallelogram is 48cm.

TO FIND:

• What is the length of the sides of a parallelogram ?

SOLUTION:

Let 'x' be common in given ratios

☆ One side = 3x

☆ Another side = 5x

To find the perimeter of parallelogram, we use the formula:-

$\bf\red{\star \: Perimeter\: of \: \parallel gram = 2(sum \:of\: measure \: of \: adjacent\: sides) \: \star }$

On putting the values in the formula, we get

$\rm{\mapsto 48 = 2( 3x + 5x) }$

$\rm{\mapsto \frac{48}{2} = ( 3x + 5x) }$

$\rm{\mapsto 24 = 8x }$

$\rm{\mapsto \frac{24}{8} = x }$

$\rm\red{\mapsto\: \star \: 3 = x \: \star }$

The value of 'x' is 3

☆ One side = 3x ☆

➨ $\sf{ One \: side = 3\times 3}$

➨ $\sf\red{\star\: One \: side = 9\:cm\: \star}$

☆ Another side = 5x ☆

➨ $\sf{ Another \: side = 5\times 3}$

➨ $\sf\red{\star\: Another \: side = 15\: cm\: \star}$

❛ Hence, the sides of a parallelogram are 9 cm and 15 cm. ❜

VERIFICATION:

➺ 48 = 2(9 + 15)

➺ 48 = 2(24)

➺ 48 = 48

[L.H.S. = R.H.S.]

Answer 2

Given ,

The ratio of adjacent sides of parallelogram is 3 : 5

The perimeter of parallelogram is 48 cm

Let , the adjacent sides of parallelogram be 3x and 5x

We know that , the perimeter of parallelogram is given by

$\sf \star \: \: Perimeter = 2(Sum \: of \: adjacent \: sides)$

Thus ,

$\sf \Rightarrow 48 = 2(3x + 5x) \\ \\ \sf \Rightarrow </p><p>24 = 8x \\ \\ \sf \Rightarrow </p><p>x = \frac{24}{8} \\ \\\sf \Rightarrow x = 3</p><p>$

$\therefore\sf \bold{ \underline{The \: sides \: of \: //gm \: are \: 9 \: cm \: and \: 15 \: cm}}$