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A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle?
Verified Answer
A rectangle and square have the same Perimeter of 100 m. Find the side...
Given:
Rectangle and square are of same perimeter that is 100 m.
To find:-
Side of square.
Length and Breadth of rectangle.
Area of rectangle.
Perimeter of square = 4a
In which 'a' is side of square.
100 = 4 x a
100/4 = a
a = 25 m.
Side of square is 25 m.
Given that,
Breadth of rectangle is a-2 ( a is side of square)
25 - 2
23 m
So, Breadth of rectangle is 23 m.
Perimeter of rectangle = 2 (l + b)
100 = 2 x (23 + l)
100 = 46 + 2l
100 - 46 = 2l
54 = 2l
54/2 = l
= 27 m.
Length of rectangle is 27 m.
Area of rectangle = l x b
27 m x 23 m
621 m^2
Area of rectangle is 621 m^2.
This question is part of UPSC exam. View all Class 6 courses
Most Upvoted Answer
A rectangle and square have the same Perimeter of 100 m. Find the side...
Given:
- Perimeter of the rectangle and square = 100 m
- Breadth of the rectangle = 2 m less than the side of the square
To find:
- Side of the square
- Length and area of the rectangle
Solution:
Let's assume the side of the square is 's' meters and the breadth of the rectangle is 'b' meters.
Perimeter of the square:
- Perimeter of a square = 4 * side
- So, 4s = 100
- Dividing both sides by 4, we get s = 25
Therefore, the side of the square is 25 m.
Length of the rectangle:
- Length of a rectangle = Perimeter of the rectangle - 2 * Breadth
- Perimeter of the rectangle = 100 m (given)
- Breadth of the rectangle = s - 2 (2 m less than the side of the square)
- Length of the rectangle = 100 - 2 * (s - 2)
Let's substitute the value of 's' into the equation:
- Length of the rectangle = 100 - 2 * (25 - 2)
- Length of the rectangle = 100 - 2 * 23
- Length of the rectangle = 100 - 46
- Length of the rectangle = 54 m
Therefore, the length of the rectangle is 54 m.
Area of the rectangle:
- Area of a rectangle = Length * Breadth
- Length of the rectangle = 54 m (calculated above)
- Breadth of the rectangle = s - 2 (2 m less than the side of the square)
- Area of the rectangle = 54 * (25 - 2)
Let's substitute the value of 's' into the equation:
- Area of the rectangle = 54 * (25 - 2)
- Area of the rectangle = 54 * 23
- Area of the rectangle = 1242 square meters
Therefore, the area of the rectangle is 1242 square meters.
Summary:
- The side of the square is 25 meters.
- The length of the rectangle is 54 meters.
- The area of the rectangle is 1242 square meters.
- Perimeter of the rectangle and square = 100 m
- Breadth of the rectangle = 2 m less than the side of the square
To find:
- Side of the square
- Length and area of the rectangle
Solution:
Let's assume the side of the square is 's' meters and the breadth of the rectangle is 'b' meters.
Perimeter of the square:
- Perimeter of a square = 4 * side
- So, 4s = 100
- Dividing both sides by 4, we get s = 25
Therefore, the side of the square is 25 m.
Length of the rectangle:
- Length of a rectangle = Perimeter of the rectangle - 2 * Breadth
- Perimeter of the rectangle = 100 m (given)
- Breadth of the rectangle = s - 2 (2 m less than the side of the square)
- Length of the rectangle = 100 - 2 * (s - 2)
Let's substitute the value of 's' into the equation:
- Length of the rectangle = 100 - 2 * (25 - 2)
- Length of the rectangle = 100 - 2 * 23
- Length of the rectangle = 100 - 46
- Length of the rectangle = 54 m
Therefore, the length of the rectangle is 54 m.
Area of the rectangle:
- Area of a rectangle = Length * Breadth
- Length of the rectangle = 54 m (calculated above)
- Breadth of the rectangle = s - 2 (2 m less than the side of the square)
- Area of the rectangle = 54 * (25 - 2)
Let's substitute the value of 's' into the equation:
- Area of the rectangle = 54 * (25 - 2)
- Area of the rectangle = 54 * 23
- Area of the rectangle = 1242 square meters
Therefore, the area of the rectangle is 1242 square meters.
Summary:
- The side of the square is 25 meters.
- The length of the rectangle is 54 meters.
- The area of the rectangle is 1242 square meters.
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A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle?
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A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle?.
A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle and square have the same Perimeter of 100 m. Find the side of the square. If the rectangle has a breadth 2 m less than that of the square find the length and area of the rectangle?.
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