Question

Two plot of a land have the same
perimeter. one is a square of side 60 m. While the other rectangle
whose breadth is 1.5 dam. which plot has the greater and by how much?
please answer fast
fo'll'ow m'e​

Answer 1

Answer:

Square perimeter = 4a = 4*60 = 240 m

Square area = 60*60 = 3600 m2

Rectangle perimeter = 2(l+b)

240 = 2(l+15)

120-15=l

l=105

Area = 105*15 = 1575m

Square has a larger area

Answer 2

Given:

• A square and a rectangle have same perimeter

• the side of the square is 60m

• the breadth of the rectangle is 1.5m

To Find:

• which one has the greater area?

Solution:

★ Understanding the concept ★

Now, here we've got the side of the square which will help us finding the perimeter of it and then we'll find the length of the rectangle. Finally let's find the area of the square and the rectangle and compare them.

${\purple{ \underline{ \mathfrak{As \: we \: know \: that : }}}} \:$

$\mapsto \sf \: perimeter \: of \: a \: square = 4 \times side$

➵ let's substitute the value of 60m instead of side

as, 60m represents the side of the square

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$\longrightarrow \sf \: perimeter \: of \: the \: square = 4 \times side \: \: \: \: \: \: \: \: \: \: \\ \\ \longrightarrow \sf \: perimeter \: of \: the \: square =4 \times 60m \: \: \: \: \: \: \: \: \: \\ \\ \longrightarrow \bf \: perimeter \: of \: the \: square =240m \bigstar$

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↦Therefore, the perimeter of the square is 240m

❍ As, perimeter of square equals perimeter of rectangle

↦ so, perimeter of the rectangle is 240m

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➺ Now, we have to find the length of the rectangle

Given,

• breath of the rectangle is 1.5m
• perimeter of the square is 240

${\purple{ \underline{ \mathfrak{As \: we \: know \: that : }}}}$

$\mapsto \sf \: \: perimeter \: of \: a \: rectangle = 2(l + b)$

───────────────────────────────

➵ let's substitute the above values and find the length

• $\blue{\implies} \sf \pink{perimeter \: of \: the \: rectangle = 2(l + b)}$

• $\blue\implies\sf\pink{240 = 2(l + 1.5)}$

• $\blue\implies\sf\pink{240 = 2l + 3}$

• $\blue\implies \sf\pink{2l = 240 - 3}$

• $\blue \implies \sf\pink{2l = 237}$

• $\blue \implies \sf\pink{l = \cancel \dfrac{237}{2} }$

• $\blue \implies \sf\pink{l = 118.5m \bigstar}$

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➛ hence the length of the rectangle is 118.5m

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❍ Now let's find the areas respectively

$\longrightarrow \tt \: area \: of \: square = {side}^{2} \: \: \\ \\ \\ \longrightarrow \tt \: area \: of \: square = {60}^{2} \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: area \: of \: square = 3600 {m}^{2}$

➛ therefore area of the square is 3600m²

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◉ Now let's find the area of the rectangle

$\longrightarrow \tt \: area \: of \:rectangle = l \times b \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \\ \\ \longrightarrow \tt \: area \: of \:rectangle = 118.5 \times 1.5\: \: \\ \\ \longrightarrow \tt \: area \: of \:rectangle = 1777.25{m} ^{2}\bigstar \: \: \:$

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➺ So, the area of the square is greater

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