Question

ucuylalt,
6. The perimeter of a parallelogram is 36 cm. The
smaller side is 8 cm long. Find the length of its
16
longer side​

Answer 1

• The length of the longer side of a parallelogram = 10 cm.

Diagram :

$\setlength{\unitlength}{19mm}\begin{picture}(6,6)\put(1,0){\line(4,5){0.8}}\put(3.1,0){\line(4,5){0.8}}\put(1,0){\line(1,0){2.1}}\put(1.8,1){\line(1,0){2.1}}\put(1.6,0.5){\bf{Perimeter = 36 cm}}\put(3.6,0.4){\bf{smaller side = 8 cm}}\put(1.1,-0.3){\bf{longer side = 10 cm}}\end{picture}$

Given :

• The perimeter of the parallelogram = 36 cm.
• The smaller side of the parallelogram (breadth) = 8 cm.

To Find :

• The length of the longer side (length) of a parallelogram.

Solution :

Let,

The length of the longer side (length) of a parallelogram be x.

Given,

The perimeter of a parallelogram is 36 cm.

The length of the smaller side (breadth) of a parallelogram is 8 cm.

We know that,

$\underline{ \boxed{ \bf{ \orange{perimeter \: of \: parallelogram = 2(l + b)}}}}$

Where,

• l = length.
• b = breadth.

We have,

• b = 8 cm.

Now, substitute the the given values in the formula of the perimeter of a parallelogram.

$: \implies \bf 36 \: cm = 2(x + 8 \: cm) \\ \\ \\ : \implies \bf \dfrac{36}{2} \: cm = x + 8 \: cm \\ \\ \\ : \implies \bf 18 \: cm = x + 8 \: cm \\ \\ \\ : \implies \bf 18 \: cm - 8 \: cm = x \\ \\ \\ : \implies \bf 10 \: cm = x \\ \\ \\ \: \: \bf \therefore \: \: x = 10 \: cm$

Hence,

The length of the longer side (length) is 10 cm.

Verification :

Given,

Perimeter of the parallelogram is 36 cm.

We know that,

$\underline{ \boxed{ \bf{ \orange{perimeter \: of \: parallelogram = 2(l + b)}}}}$

Now we have,

• The length of the parallelogram (longer side) = 10 cm.
• The breadth of the parallelogram (smaller side) = 8 cm.

Now, substitute the values in the formula of the parallelogram.

$: \implies \bf 36 \: cm = 2(10\: cm +8 \: cm) \\ \\ \\ : \implies \bf 36 \: cm = 2(18 \: cm) \\ \\ \\ : \implies \bf 36 \: cm = 2 \times 18 \: cm \\ \\ \\ : \implies \bf 36 \: cm = 36 \: cm$

Hence Verified !