Question: The perimeter of a square is equal to the perimeter of a rectangle whose length and width are 6m and 4m, respectively. The side of the square is:
(A) 3m
(B) 4m
(C) 5m
(D) 6m
(E) 7m
The Perimeter of a Square is Equal to the Perimeter of a Rectangle Whose Length And Width are 6m and 4m Respectively GMAT Problem Solving - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Course, 2021”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical understanding.
Solution and Explanation:
Approach Solution 1:
Explanation: Given in the question that the perimeter of a square is equal to the perimeter of a rectangle.
The width and length of the rectangle are 4m and 6m respectively.
It has asked to find out the side of the square.
A perimeter is the sum of all the sides of the quadrilateral.
For the case of a rectangle, it has four sides and the opposite sides are parallel and equal to each other.
Let l be the length of the side of the rectangle.
Let b be the breadth of the rectangle.
Given: l = 6m
b = 4m
Now it is known that a rectangle has four sides and opposite sides of a rectangle are equal. So the perimeter of the rectangle = sum of all the four sides
P = 6m + 6m + 4m + 4m = 12m + 8m = 20m
The perimeter of the rectangle is found to be 20m
Now it is given that the perimeter of the square is equal to the perimeter of the rectangle.
Let x be the side of the square. It is known that a square has four sides and all the sides are equal
So the perimeter of a square = 4*x
Now this perimeter is equal to the perimeter of the rectangle
4x = 20
X = 20/4 = 5
The length of the side of the square is 5m. Therefore option C is the correct answer.
Correct Answer: C
Approach Solution 2:
Explanation:
The perimeter of rectangle is 2*(l+b)
Where l = length of the rectangle and b = breadth of the rectangle
Let side of square be a
Perimeter of square = 4*a
We get,
4*a = 2(l + b) (perimeter of square = perimeter of the rectangle)
4*a = 2(6m + 4m)
a = 2*(10m)/4m
a = 5m
The length of the side of the square is 5m. Therefore the correct option is C.
Correct Answer: C
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