Question

Your answer
2 points
11) The perimeter of a rectangle is
13 cm and its width is 11/4cm find
its length​

Answer 1

Perimeter of a rectangle = 13cm

2( length + breadth) =13

length+11/4=13/2

length=13/2-11/4

length=26/4-11/4

length=(26-11)/4

length=15/4

Therefore, length of the rectangle=15/4cm

Answer 2

• The length of the rectangle = 15 / 4 cm.

Given :

• The perimeter of the rectangle = 13 cm.
• The width of the rectangle = 11 / 4 cm.

To Find :

• The length of the rectangle.

Solution :

Let,

The length of the rectangle be x.

Given,

The perimeter of the rectangle is 13 cm.

We know that,

Perimeter of the rectangle = 2 ( l + b )

Where,

• l = length = ?
• b = breadth = 11 / 4 cm.

Now, substitute the given values in the formula of perimeter of the rectangle.

$: \implies \bf{13 \: cm = 2(x + \dfrac{11}{4} \: cm)} \\ \\ \\ : \implies \bf{ \dfrac{13}{2} \: cm = x + \dfrac{11}{4} \: cm } \\ \\ \\ : \implies \bf{ \dfrac{13}{2} \: cm - \dfrac{11}{4} \: cm = x } \\ \\ \\ : \implies \bf{ \dfrac{13 \times 2 - 11 \times 1}{4} \: cm = x} \\ \\ \\ : \implies \bf{ \dfrac{26 - 11}{4} \: cm = x} \\ \\ \\ : \implies \bf{ \dfrac{15}{4} \: cm = x} \\ \\ \\ \: \: \bf \therefore \: \: { length = \dfrac{15}{4} \: cm}$

Hence,

The length of the rectangle is 15 / 4 cm.

Verification :

Given,

• The perimeter of the rectangle = 13 cm.

We know that,

Perimeter of the rectangle = 2 ( l + b )

Where,

• l = length = 15 / 4 cm.
• b = breadth = 11 / 4 cm.

Now, substitute all the values in the formula of perimeter of the rectangle.

$: \implies \bf{13 \: cm = 2 \bigg( \dfrac{15}{4} \: cm + \dfrac{11}{4} \: cm \bigg)} \\ \\ \\ : \implies \bf{13 \: cm = 2 \bigg( \dfrac{15 + 11}{4} \: cm \bigg) } \\ \\ \\ : \implies \bf{13 \: cm = 2 \bigg( \dfrac{26}{4} \: cm \bigg)} \\ \\ \\ : \implies \bf{13 \: cm = \not{ 2} \bigg( \dfrac{13}{ \not{2}} \: cm\bigg) } \\ \\ \\ : \implies \bf{13 \: cm = 1 \times 13 \: cm} \\ \\ \\ : \implies \bf{13 \: cm = 13 \: cm}$

Hence Verified !