Question

the difference between the length and breadth of a rectangle is 23 m. If the perimeter is 206 m, then it's area is​

Answer 1

let let the breath be x

length=X + 23

perimeter=2 (l+b)

206=2 ( X + 23 + x)

206=4x+46

206 -46=4x

X=160/4=40=breath

length=40+23=63

area=40*63=2520

Answer 2

AnswEr:

GivEn:

• Difference of Length & Breadth - 23m
• Perimeter (Rectangle) = 206 m

To Find:

• Area of the Rectangle - ?

Formula Used:

$\\ \bullet \: \: \: \bf \purple{\sf{Perimeter_{(Rectangle)} = 2(l+b) }} \\ \\ \bullet \: \: \: \bf \purple{\sf{Area_{(Rectangle)} = (Length \times Breadth) }}$

Solution:

Let assume the length of rectangle be x.

again,

Breadth be ( x - 23)m.

Now,

$\implies\sf { 206 = 2 (x +(x-23)) } \\ \\ \implies\sf{ 206 = 2 (2x - 23) } \\ \\ \implies\sf{ 206 = 4x - 46} \\ \\ \implies\sf{ 206 + 46 = 4x } \\ \\ \implies\sf{ 4x = 252 } \\ \\ \implies{\sf{ x = \dfrac{ \cancel{252}^{ \: \: 63}}{ \cancel{4}} }} \\ \\ \implies\sf{ x = 63}$

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Thus,

Length = x

$\colon\longrightarrow\sf{ 63\:m}$

Breadth be = (x - 23)

$\colon\longrightarrow\sf{ 63 -23} \\ \colon\implies\sf{ 40\:m}$

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Area of the Perimeter = Length × Breadth

$\colon\longrightarrow\sf{ 63 \times 40} \\ \colon\implies\sf{ 2520\:m^2}$