Question

The perimeter of a rectangle is 10 times its breadth. If the length of rectangle is 4 times the breadth where perimeter is 100 cm, then the area of rectangle is

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Answer 1

Answer:

400 cm²

Step-by-step explanation:

As per the provided information in the given question, we have :

• Perimeter of the rectangle = 10 times its breadth
• Length = 4 times the breadth
• Perimeter = 100 cm

We've been asked to calculate the area of rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀» According to the question, the perimeter of a rectangle is 10 times its breadth and the length of rectangle is 4 times the breadth. So, firstly let's suppose the breadth as b. Now, as the perimeter of a rectangle is 10 times its breadth. Henceforth,

$\dashrightarrow \quad \rm { Perimeter = 10b}$

Also, according to the question the perimeter of the rectangle is 100 cm.

$\dashrightarrow \quad \rm { Perimeter = 100 \; cm}$

We can say that,

$\dashrightarrow \quad \rm { 10b = 100 \; cm}$

Now, transposing 10 from LHS to RHS in order to calculate the value of b. As, 10 is in the form od multiplication in LHS, it'll become in the form of division in RHS.

$\dashrightarrow \quad \rm { b = \cancel{\dfrac{ 100 \; cm}{10}} }$

Cancelling the terms.

$\dashrightarrow \quad \boxed{ \bf { b = 10 \; cm}}$

Therefore the breadth of the rectangle is 10 cm.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀» Now, according to the question the length of rectangle is 4 times the breadth. So, length will be 4b. Now, substitute the value of b.

$\dashrightarrow \quad \rm { \ell = 4(10) \; cm}$

$\dashrightarrow \quad \boxed{ \bf { \ell = 40 \; cm}}$

Therefore, the length of the rectangle is 40 cm.

Now, we have to find the area of the rectangle.

$\bigstar \quad \underline{ \boxed{ \bf { Area_{(Rectangle)} = \ell \times b}}}$

• l denotes length
• b denotes breadth

Substitute the values.

$\dashrightarrow \quad \rm { Area_{(Rectangle)} = 10 \; cm \times 40 \; cm}$

$\dashrightarrow \quad \underline{ \boxed{ \bf { Area_{(Rectangle)} = 400 \; cm^2 }}}$

Therefore, area of the rectangle is 400 cm².

$\rule{200}2$

Answer 2

Given:

$\red\bigstar$Perimeter is 10 times the breadth.

$\red\bigstar$Length is 4 times the breadth.

$\red\bigstar$Perimeter is 100 cm.

$\rule{160pt}{1pt}$

To Find:

$\red\bigstar$Area of the rectangle.

$\rule{160pt}{1pt}$

Solution:

$\sf{Let\:the\:breadth\: be\: x\: cm}.$

$\sf{Then\: perimeter\: will \:be\: 10x \:cm}.$

$\sf{But,\:perimeter\: is\: given\: 100\: cm. Then, }$

$\sf{\:\:\:\:\:\:\:=> 10x=100 \:cm}$

$\sf{\:\:\:\:\:\:\:=> x=\frac{100}{10}=\frac{10}{1}=10\:cm}$

$\sf{Hence,\:value\: of \:breadth \:is \:10\: cm}.$

$\rule{160pt}{1pt}$

$\sf{Now,\:as\: we\: have \:said\: earlier\: :-}$

$\sf{length=4×breadth}$

$\sf{\:\:\:\:\:\:\: => 4×10={40 cm}^2}$

$\rule{160pt}{1pt}$

$\sf{Now,\:formula\: for \:area \:of\: a\: rectangle :-}$

$\sf{\fbox{Area(Rectangle)}\:\:length × breadth}$

$\sf{\:\:\:\:\:\:\:=> 40×10}$

$\sf{\:\:\:\:\:\:\:=> {400}^2}$

$\sf{So,\:area \:of \:the\: rectangle\: is\: {400}^2}$

$\red{\rule{65pt}{1pt}}\blue{\rule{65pt}{1pt}}\green{\rule{65pt}{1pt}}$