Question

The length of rectangle is 15 cm more than its width.Its perimeter is 70 cm. Find the dimensions of rectangle. ​

Answer 1

$\large \purple {\sf {Given:}}$

The length of a rectangle is 15 cm more than it's width.

It's perimeter is 70 cm.

$\large \pink {\sf {To \: Find:}}$

The dimensions of rectangle.

$\large \red {\sf {Assumption:}}$

Let the width be x, so that

length = 15 + x

width = x

$\large \green {\sf {Formula:}}$

Perimeter of rectangle = 2 ( l + b )

$\large \blue {\sf {Solution:}}$

By putting the values , we get

2 ( 15 + x + x ) = 70

or, 30 + 4x = 70

or, 4x = 70 - 30

or, x = 40/4

or, x = 10

$\huge \orange {\sf {Answer:}}$

Length = x + 15 = 10 + 15 = 25 cm

Width = x = 10 cm

Answer 2

$\sf\large\underline\red{Let:}$

$\sf{\implies Length\:_{(rectangle)}=x+15}$

$\sf{\implies Breadth\:_{(rectangle)}=x}$

$\sf\large\underline\red{To\: Find:}$

$\rm{\implies Dimensions\:_{(rectangle)}=?}$

$\sf\large\underline\red{Solution:}$

• As you know that in the given Question we have to find out the dimensions of rectangle. To calculate the dimensions of rectangle at first we have to assume the breadth of rectangle be x cm and the length of rectangle be x+15 cm. After we have to apply the formula of perimeter of rectangle then we get the dimensions of rectangle:]

$\sf\large\underline\purple{Here\:\:P=70cm\:\:,L=x+15\:\:B=x:}$

$\sf\large\underline\red{Formula\: used:}$

$\sf{\implies Perimeter\:_{(rectangle)}=2(length+breadth)}$

$\tt{\implies 2(x+15+x)=70}$

$\tt{\implies 2(2x+15)=70}$

$\tt{\implies 4x+30=70}$

$\tt{\implies 4x=70-30}$

$\tt{\implies 4x=40\implies x=10cm}$

• Now calculate the dimensions here:]

$\sf\large{Hence,}$

$\sf{\implies Length\:_{(rectangle)}=x+15=25cm}$

$\sf{\implies Breadth\:_{(rectangle)}=x=10cm}$

• Some additional formula for rectangle:]

$\sf{\implies Area\:_{(rectangle)}=length*breadth}$

$\sf{\implies Diagonal\:_{(rectangle)}=length^2+breadth^2}$

$\sf{\implies Breadth\:_{(rectangle)}=\frac{Area}{length}}$

$\sf{\implies Length\:_{(rectangle)}=\frac{Area}{breadth}}$