Question

A Square and a rectangle have equal perimeter .The side of the square is 60cm and the length of the rectangle is thrice its breadth.Which shape has greater area and by how much?​

Answer 1

Answer:

Explanation:

Given :

• Perimeter of square = Perimeter of rectangle.
• Side of square is 60 cm.
• Length of the rectangle is thrice its breadth.

To Find :

• Which shape has greater area and how much?

Solution :

Given that, Perimeter of square = Perimeter of rectangle

=> 4 × 60 = Perimeter of rectangle

=> Perimeter of rectangle = 240 cm

Given that, Length of the rectangle is thrice its breadth.

.°. l = 3b

=> Perimeter of rectangle = 2(l + b)

=> 240 = 2(3b + b)

=> 240 = 2(4b)

=> 240 = 8b

=> b = 30

So,

Length of rectangle = 3b = 3 × 30 = 90 cm Now,

Area of square = side²

=> Area of square = 60²

=> Area of square = 3600 cm²

Area of rectangle = l × b

=> Area of rectangle = 90 × 30

=> Area of rectangle = 2700 cm²

.°. 3600 > 2700

Hence :

Square shape has greater area , 3600 cm².

Answer 2

Question :-

A Square and a rectangle have equal perimeter. The side of the square is 60 cm and the length of the rectangle is thrive it's breadth. Which shape has greater area and by how much ?

Given :-

$\star \sf \: side \: of \: square \: = 60 \: cm \\ \\ \star \sf \: peimeter \: of \: rectangle = perimeter \: of \: square \\ \\ \star \sf \: length \: of \: rectangle \: is \: thrice \: of \: \\ \sf \: its \: breadth$

Solution :-

Let the side of square is x , then

$\star \sf \: x = 60 \: cm$

We know that ,

• $\sf \: perimeter \: of \: square = 4x$

$\star \sf \: where \: x \: is \: the \: side \: of \: square$

So ,

$\star \sf \: perimeter \: of \: square \: = 4 \times 60 \\ \\ \implies \sf \: 240 \: cm$

But , Perimeter of square = Perimeter of Rectangle (Given)

So,

$\star \sf \: perimeter \: of \: rectangle = 240 \: cm$

Let , the length of the rectangle is l and Breadth of the rectangle is w.

We know that ,

• $\sf \: perimeter \: of \: rectangle = 2(l + w)$

$\star \sf \: where \: l \: is \: the \: length \: of \: rectangle \\ \\ \star \sf \: w \: is \: the \: breadth \: of \: rectangle$

So,

$\sf \: 2(l + w) = 240 - - - (i)$

According to the Question,

The length of the rectangle is thrice of it's breadth. So,

$\star \sf \: l = 3 w$

Substituting the value of l into Equation (i) -

$\implies \sf \: 2(3w + w) = 240 \\ \\ \implies \sf3w + w = \frac{240}{2} \\ \\ \implies \sf4w = 120 \\ \\ \implies \sf \: w = \frac{120}{4} \\ \\ \implies \boxed{ \sf \: w = 30 \: cm}$

The breadth of the rectangle is 30 cm so the length of the rectangle is ,

$\sf \: l = 3 \times w \\ \\ \implies \sf \: l = 3 \times 30 \\ \\ \implies \boxed{ \sf \: l = 90 \: cm}$

The length of the rectangle is 90 cm .

We know that ,

• $\sf \: area \: of \: square = {side}^{2}$
• $\sf \: area \: of \: rectangle = l \times w$

So,

$\star \sf \: area \: of \: square = {(60)}^{2} \\ \\ = \: \sf \: 3600 \: {cm}^{2}$

$\star \sf \: area \: of \: rectangle = 30 \times 90 \\ \\ = \sf \: 2700 \: {cm}^{2}$

As we can se that Area of Square is greater than Area of Rectangle.

So the Rectangle has greater area of 3600 cm².

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Hope it will help you :)