A square and a rectangle field with measurement as given in the figure have the same perimeter. Which field has a larger area?

Last updated date: 26th Mar 2023
•
Total views: 308.1k
•
Views today: 5.85k
Answer
308.1k+ 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
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

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

A Short Paragraph on our Country India
