Answer

Verified

476.7k+ views

Hint: First find the other side of the rectangle by equating the perimeter of square and rectangle. Now use formula for area of square and rectangle to get the final answer.

Complete step-by-step answer:

It is given that perimeter of rectangle = perimeter of square.. (1)

Step 1: Let us suppose that side of square = s

Perimeter of square = $60 + 60 + 60 + 60 = 240$= (4s)

From (I)

$

2\left( {l + b} \right) = 240 \\

\Rightarrow 2\left( {80 + b} \right) = 240 \\

\Rightarrow 160 + 2b = 240 \\

\Rightarrow 2b = 240 - 160 \\

\Rightarrow 2b = 80 \\

\Rightarrow b = 40 \\

\\

$

So, $l = 80,{\text{ b = 40}}$

Step 2: Now we have to find out whether the area of square has the larger area or the area of rectangle has the larger area:

We know that:

Area of square=$side \times side$

=$

60 \times 60 \\

= 3600 \\

$

Area of rectangle= $l \times b$

$

= 80 \times 40 \\

= 3200 \\

$

Therefore, the area of the square is greater than the area of the rectangle that is 3600.

Note: Whenever we face such types of questions, the key concept is that we have to first calculate the perimeter of the square then the perimeter of the rectangle. First, we calculate the perimeter of the square like we did in the question. With the help of the perimeter of the square we will calculate the breadth of the rectangle by applying the formula$2\left( {l + b} \right)$. Second step is to calculate the area of the rectangle and area of square and to check whether the fig a has the larger area or the fig b has the larger area. After applying the formula we get our required answer , like in the above question the area of the square is greater than the area of the rectangle.

Complete step-by-step answer:

It is given that perimeter of rectangle = perimeter of square.. (1)

Step 1: Let us suppose that side of square = s

Perimeter of square = $60 + 60 + 60 + 60 = 240$= (4s)

From (I)

$

2\left( {l + b} \right) = 240 \\

\Rightarrow 2\left( {80 + b} \right) = 240 \\

\Rightarrow 160 + 2b = 240 \\

\Rightarrow 2b = 240 - 160 \\

\Rightarrow 2b = 80 \\

\Rightarrow b = 40 \\

\\

$

So, $l = 80,{\text{ b = 40}}$

Step 2: Now we have to find out whether the area of square has the larger area or the area of rectangle has the larger area:

We know that:

Area of square=$side \times side$

=$

60 \times 60 \\

= 3600 \\

$

Area of rectangle= $l \times b$

$

= 80 \times 40 \\

= 3200 \\

$

Therefore, the area of the square is greater than the area of the rectangle that is 3600.

Note: Whenever we face such types of questions, the key concept is that we have to first calculate the perimeter of the square then the perimeter of the rectangle. First, we calculate the perimeter of the square like we did in the question. With the help of the perimeter of the square we will calculate the breadth of the rectangle by applying the formula$2\left( {l + b} \right)$. Second step is to calculate the area of the rectangle and area of square and to check whether the fig a has the larger area or the fig b has the larger area. After applying the formula we get our required answer , like in the above question the area of the square is greater than the area of the rectangle.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths