Question

Area of a square plot is 1225m².Its perimeter is equal to the perimeter of a rectangular plot, whose length is 10m greater than
the breadth. Find the area of the rectangular plot.​

Answer 1

Solution!!

Area of a square plot is given. It is also given that the perimeter of the square plot is equal to the perimeter of the rectangular plot.

Area of square plot = 1225 m²

Area = (Side)²

1225 m² = (Side)²

Side = 35 m

Perimeter of the square plot = 4 × Side

Perimeter = 4 × 35 m

Perimeter = 140 m

Perimeter of rectangular plot = 140 m

It is given that the length of the rectangular plot is 10m more than the breadth.

Let the breadth be x.

Length = x + 10 m

Perimeter = 2(Length + Breadth)

140 m = 2(x + 10 m + x)

140 m = 2(2x + 10 m)

140 m = 4x + 20 m

140 m - 20 m = 4x

120 m = 4x

x = 120 ÷ 4

x = 30 m

Breadth = x = 30 m

Length = x + 10 m = 30 m + 10 m = 40 m

We know the length and breadth of the rectangular plot. We have to find its area.

Area = Length × Breadth

Area = 40 m × 30 m

Area = 1200 m²

Answer 2

Concept used :-

Here the concept of Perimetre and area is used.

First we will find the side of the square. Then we will find the perimeter of square and rectangle. Equate both the Perimetre and will get the breath. Find the length and finally subsitute the value of length and breath in area formula of rectangle to get the desired result.

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Formula used:-

$\bull \bold \orange{Area\:of \: rectangle= length×breath}$

$\bull \bold \pink{Area \: of \: square = side²}$

$\bull \bold \purple{perimeter \:of \: rectangle =2 (length× breath )}$

$\bull \bold \blue{perimeter\:of \: Square= 4×side}$

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Solution

$\sf{ \color{grey}Area \: of \: square \: plot = side²}$

$\sf{ \implies1225= side²}\\ \ \sf{ \implies side = √1225}\\ \\ \sf{ \implies \color{green}side = 35 metre.}$

$\sf{ \implies \color{grey}Perimeter \: of \: square = 4× side } \\ \\ \sf{ \implies perimeter\:of\: square = 4 × 35 } \\ \\ \sf{ \implies \color{red}perimeter\:of \: square = 140 \: metre}$

Now

Let us assume breath of the rectangular plot as x m.

➜Length of rectangular plot =( 10+x ) m

$\sf{ \color{grey}perimeter \: of \: rectangle \: plot = 2(l+b)}$

where

• l denotes length
• b denotes Breath

$\sf{ \implies perimeter \: of \: rectangular \: plot = 2( x+x+10)} \\ \sf{ \implies perimeter \: of \: rectangular \: plot = (4x +20 ) metre}$

It's is given that ::-

$\sf\red{Perimeter\:of\:Square \: plot = Perimetre\: of \:rectangular\:plot }$

$\sf{ \implies \: 140 = 4x+20} \\ \\ \sf{ \implies120 = 4x } \\ \\ \sf{ \implies x= \frac{120}{4}} \\ \\ \sf{ \implies \color{green}x= 30 metre }$

therefore the breath is of 30 metre

➜length = x+10 = 30 +10 = 40 metre

According to the question, we have to find the area of rectangle

$\sf{ \color{grey}Area\:of \:rectangle= length×breath}\\ \\ \sf{ \implies Area\:of\:rectangle= 30 ×40}\\ \\ \sf{\implies \color{red}Area\:of\: rectangle=1200 m²}$

Therefore the area of the rectangular plot is 1200m².

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