Question

two plots of land have same perimeter one is a square of side 60 m while other is rectangle whoose breadth is 15 m which plot has greater area​

Answer 1

Answer:

The square plot

Step-by-step explanation:

side of square=60m

perimeter of square=60x4=240m

now perimeter of squjare and rectangle are both equal

we have only breadth of rectangle so lets remove the length.

let length is x.

so 2(x+15)=240

so 2x+30=240

2x=210

x=105m

Area of square is s²=60²=3600m²

area of rectangle is l×b=105×15=1575m²

as 3600>1575

thus the area of the square plot is greater than that of the rectangular plot.

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Answer 2

Answer :-

• The plot of square encloses more area than Rectangle.

Step-by-step explanation ::

To Find :-

• Which plot has greater area

Given that,

• Two plots of same perimeter, one is square and the other is rectangle
• Side of square = 60m
• Breadth of rectangle = 15m

Solution:

The perimeter of square is,

$\underline{ \boxed{\sf{ \red{{Perimeter}_{(square)} = 4 \times side}}}}$

Therefore,

$\sf{ \longmapsto \: {Perimeter}_{(square)} = (4 \times 60)m} \\ \\ \\ \bf{ \longmapsto \: {Perimeter}_{(square)} = 240m} \: \: \: \:$

• The perimeter of square is 240m

Given that,

Perimeter of square = Perimeter of rectangle,

Hence, the perimeter of rectangle is 240m.

Now, we need to find out the length of rectangle, and we can find it by applying the formula of perimeter of rectangle,

As we know that,

$\underline{ \boxed{\sf{ \red{{Perimeter}_{(rectangle)} = 2(length \: + breadth)}}}}$

Therefore,

$\sf{ \longmapsto \: {2(length + 15) = 240}} \\ \\ \\ \sf{ \longmapsto \: length + 15= \dfrac{240}{2}} \: \: \: \: \\ \\ \\ \sf{ \longmapsto \: length + 15= \cancel{\dfrac{240}{2}}} \: \: \: \\ \\ \\ \sf{ \longmapsto \: length + 15= 120} \: \: \: \: \\ \\ \\ \sf{ \longmapsto \: length = 120 - 15} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf{ \longmapsto \: length = 105} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \bf{ \longmapsto \: length = 105} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Therefore, the length of rectangle is 105m.

According the question,

• The area of square is,

As we know that,

$\underline{ \boxed{\sf{ \red{{Area}_{(square)} = side \times side}}}}$

Therefore,

$\sf{ \longmapsto \: {Area}_{(square)} = (60 \times 60){m}^{2}} \\ \\ \\ \bf{ \longmapsto \: {Area}_{(square)} = {3600m}^{2}} \: \: \: \: \: \:$

Now,

• The area of rectangle is,

As we know that,

$\underline{ \boxed{\sf{ \red{{Area}_{(rectangle)} = (length \: \times breadth)}}}}$

Therefore,

$\sf{ \longmapsto \: {Area}_{(rectangle)} = (105 \times 15){m}^{2}} \\ \\ \\ \bf{ \longmapsto \: {Area}_{(rectangle)} = {1575m}^{2}} \: \: \: \: \: \:$

Hence,The plot of square encloses more area than Rectangle

=> 3600m² > 1575m²

=> Area of square plot > Area of Rectangular plot.