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The area of a square is 1521 sq. m. The breadth of a rectangle is ⅓ times the side of the square and the length of the rectangle is twice the breadth. What is the difference between the areas of the square and the rectangle?
- a)1183 m2
- b)1300 m2
- c)1365.3 m2
- d)1452 m2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The area of a square is 1521 sq. m. The breadth of a rectangle is ⅓ t...
Area of the square = 1521 sq. m
∴ Side of the square = 
Breadth of the rectangle 
Length of the rectangle = 2 × 13 m
Area of the rectangle
Now, difference between the areas of the square and the rectangle = 1521 - 338 = 1183 m2
∴ The difference between the areas of the square and the rectangle is 1183 m2.
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The area of a square is 1521 sq. m. The breadth of a rectangle is ⅓ t...
Given information:
- The area of a square is 1521 sq. m.
- The breadth of a rectangle is ⅓ times the side of the square.
- The length of the rectangle is twice the breadth.
To find:
The difference between the areas of the square and the rectangle.
Solution:
Step 1: Find the side length of the square
Let the side length of the square be 's'.
Given, the area of the square is 1521 sq. m.
So, s^2 = 1521
Solving for 's', we get s = √1521 = 39 m.
Step 2: Find the breadth of the rectangle
The breadth of the rectangle is ⅓ times the side of the square.
So, breadth = (1/3) * 39 = 13 m.
Step 3: Find the length of the rectangle
The length of the rectangle is twice the breadth.
So, length = 2 * 13 = 26 m.
Step 4: Find the area of the square
The area of the square is s^2 = 39^2 = 1521 sq. m.
Step 5: Find the area of the rectangle
The area of the rectangle is length * breadth = 26 * 13 = 338 sq. m.
Step 6: Find the difference between the areas of the square and the rectangle
Difference = Area of square - Area of rectangle = 1521 - 338 = 1183 sq. m.
Therefore, the difference between the areas of the square and the rectangle is 1183 sq. m. (Option A).
- The area of a square is 1521 sq. m.
- The breadth of a rectangle is ⅓ times the side of the square.
- The length of the rectangle is twice the breadth.
To find:
The difference between the areas of the square and the rectangle.
Solution:
Step 1: Find the side length of the square
Let the side length of the square be 's'.
Given, the area of the square is 1521 sq. m.
So, s^2 = 1521
Solving for 's', we get s = √1521 = 39 m.
Step 2: Find the breadth of the rectangle
The breadth of the rectangle is ⅓ times the side of the square.
So, breadth = (1/3) * 39 = 13 m.
Step 3: Find the length of the rectangle
The length of the rectangle is twice the breadth.
So, length = 2 * 13 = 26 m.
Step 4: Find the area of the square
The area of the square is s^2 = 39^2 = 1521 sq. m.
Step 5: Find the area of the rectangle
The area of the rectangle is length * breadth = 26 * 13 = 338 sq. m.
Step 6: Find the difference between the areas of the square and the rectangle
Difference = Area of square - Area of rectangle = 1521 - 338 = 1183 sq. m.
Therefore, the difference between the areas of the square and the rectangle is 1183 sq. m. (Option A).
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