Question

The length of a rectangle is 15 cm more than its width eand it's perimeter is 150 cm . find the deminsions of the rectangle ?

Answer 1

$\huge{\underbrace{\text{Question}}}$

The length of a rectangle is 15 cm more than its width and it's perimeter is 150 cm . find the deminsions of the rectangle.

$\huge{\underbrace{\text{Answer}}}$

Given:-

$\sf{\rightarrow{The\:length\:is\:15\:more \:than \: the \: width \: of \: the \: rectangle}}.$

$\sf{\rightarrow{Perimeter \: of \: the \: rectangle \: is \: 150cm}}$

To Find:-

$\sf{\rightarrow{The \: deminsions \: of \: the \: rectangle}}$

Solution:-

Let the length of the rectangle be x

Therefore,

The width of the rectangle = (x+15)

As we know that,

$\boxed{\sf{\blue{\bold{Perimeter \: of \: a \: rectangle} = 2(l + b)}}}$

Where,

• l stands for length
• b stands for breadth/width

According to the question,

$\sf{2\{(x) + (x + 15)\} = 150}$

$\\ \sf{\implies{2(x + x + 15) = 150}}$

$\\ \sf{\implies{2(2x + 15) = 150}}$

$\\ \sf{\implies{4x + 30= 150 }}$

$\\ \sf{\implies{4x = 150 - 30}}$

$\\ \sf{\implies{x = \frac{120}{4}}}$

$\\ \sf{\therefore{\orange{x = 30}}}$

Hence, length = 30cm

Therefore,

Width of the rectangle = (30+15)cm=45cm

$\underline{\boxed{\rm{Hence, length \: of \: the \: rectangle = 30cm}}}$

$\underline{\boxed{\rm{Width \: of \: the \: rectangle = 45cm}}}$

Answer 2

Given :

• Length of a rectangle = 15 cm
• Width and the perimeter = 150 cm

To find

• Deminsions Of The Rectangle

Solution :

Let ,

The width of the rectangle be x cm

Then ,

Length = x ( x + 15 ) cm

Perimeter = 2 ( Length + width )

= 2 ( x + 15 + x ) cm

= 2 ( 2x + 15 ) cm

= 4x + 30 cm

But ,

The perimeter is given as 150 cm

Therefore ,

4x + 30 = 150

==] 4x = 150 - 30

==] 4x = 120

$x = \frac{120}{4} = 30 \: cm$

Hence , width of the rectangle = 30 cm and length of the rectangle = ( 30 + 15 ) cm = 45 cm

Check

We have ,

Length = 45 cm

Width = 30 cm

Therefore ,

Perimeter = 2 ( Length + width )

= 2 ( 45 + 30 ) cm

= 2 × 75 = 150 cm

Which is the same given in the problem

Also , Length is 15 cm more than the width , which is also the same as given in the problem .