Question

The adjacent sides of a parallelogram are in the ratio 3:7 and the perimeter

Is 100cm. Find the sides of the parallelogram.​

Answer 1

[ REFER TO THE ATTACHMENT ]

Here, given that

• Adjacent sides of a parallelogram are in the ratio 3 : 7.
• Perimeter of the parallelogram is 100cm.

Put k in the ratio of the adjacent sides of the parallelogram.

• First side = BC = 3k
• Second side = AB = 7k

Let

• BC = a
• AB = b

As we know that perimeter of a parallelogram is 2 (a + b)

Now, according to question :

➥ 2 (3k + 7k) = 100

➥ 2 (10k) = 100

➥ 20k = 100

➥ k = 100/20

➥ k = 5

Put the value of k in the ratio.

• First side = BC = AD = 3k = 3(5) = 15 units
• Second side = AB = CD = 7k = 7(5) = 35 units

[ Since, opposite sides of a parallelogram are equal, So, BC = AD and AB = CD ]

Hence,all sides of the parallelogram are 15 units, 35 units, 15 units and 35 units respectively.

Answer 2

${\huge{\rm{\underline{\underline{Question:-}}}}}$

Q) The adjacent sides of a parallelogram are in the ratio 3:7 and the perimeter is 100 cm . Find the sides of the parallelogram .

${\huge{\rm{\underbrace{Answer\checkmark}}}}$

$\bf{Given}\begin{cases}\sf{It \;is \; a \; \bf{parallelogram}.}\\ \sf{Ratio\;of\;adjacent\;sides=\bf{3:7}}\\ \sf{Perimeter=\bf{100cm}}\end{cases}$

To Find :-

• The sides of parallelogram .

Solution :-

# Consider a parallelogram ABCD in which ,

• AB = CD &
• BC = AD

${\textit{\textbf{According\;to\;the\; Question:}}}$

• BC : AB = 3 : 7

Or

• CD : AD = 3 : 7

Let the ratios be 3x & 7x

so ,

• AB = CD = 7x
• BC = AD = 3x

As we know ,

$\: \: \: \: \: \: \: \: \: \boxed{ \sf{perimeter = sum \: of \: all \: sides}}$

So , Here ,

${\rm{\mapsto\;Perimeter = AB+BC+CD+AD}}$

$\mapsto \rm \: 100 \: cm = 7x + 3x + 7x + 3x$

$\mapsto \rm \: \cancel{100} \: cm = \cancel{20}x$

$\mapsto \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \rm{ \pink{x = 5 \: cm}}}}$

So ,

Sides of the parallelogram would be :

• AB = CD = 7×5 cm = 35 cm .
• BC = AD = 3×5 cm = 15 cm .

NOTE : The opposite sides of a parallelogram are equal in length and are parallel .