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The perimeter of a rectangular field is 120 m and the difference between its two adjacent sides is 40 m. The sides of the square field whose area is equal to this rectangular field is?
- a)15√3
- b)10√3
- c)15√5
- d)10√5
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The perimeter of a rectangular field is 120 m and the difference betwe...
Perimeter of rectangle = 2(l + b) = 120
l + b = 60m — (1)
l – b = 40m –(2)
From (1) and (2)
l = 50 m; b = 10m
Area of rectangle = 500m² = Area of Square
Side of a square = 10√5
l + b = 60m — (1)
l – b = 40m –(2)
From (1) and (2)
l = 50 m; b = 10m
Area of rectangle = 500m² = Area of Square
Side of a square = 10√5
Most Upvoted Answer
The perimeter of a rectangular field is 120 m and the difference betwe...
Let's assume that the length of the rectangular field is L and the width is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
Given that the perimeter of the rectangular field is 120 m, we can set up the equation: 2L + 2W = 120.
We are also given that the difference between the two adjacent sides of the rectangle is 40 m, so we can set up another equation: L - W = 40.
Solving these two equations simultaneously will give us the values of L and W.
From the second equation, we can express L in terms of W: L = W + 40.
Substituting this value of L into the first equation, we get: 2(W + 40) + 2W = 120.
Simplifying this equation, we get: 2W + 80 + 2W = 120.
Combining like terms, we get: 4W + 80 = 120.
Subtracting 80 from both sides, we get: 4W = 40.
Dividing both sides by 4, we get: W = 10.
Substituting this value of W back into the equation L = W + 40, we get: L = 10 + 40 = 50.
So, the length of the rectangular field is 50 m and the width is 10 m.
The area of the rectangular field is given by the formula: A = L * W = 50 * 10 = 500 m^2.
The area of a square is given by the formula: A = side^2.
Setting up an equation to find the side length of the square, we get: side^2 = 500.
Taking the square root of both sides, we get: side = sqrt(500) = 10sqrt(5).
Therefore, the sides of the square field whose area is equal to the rectangular field are 10sqrt(5) m.
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
Given that the perimeter of the rectangular field is 120 m, we can set up the equation: 2L + 2W = 120.
We are also given that the difference between the two adjacent sides of the rectangle is 40 m, so we can set up another equation: L - W = 40.
Solving these two equations simultaneously will give us the values of L and W.
From the second equation, we can express L in terms of W: L = W + 40.
Substituting this value of L into the first equation, we get: 2(W + 40) + 2W = 120.
Simplifying this equation, we get: 2W + 80 + 2W = 120.
Combining like terms, we get: 4W + 80 = 120.
Subtracting 80 from both sides, we get: 4W = 40.
Dividing both sides by 4, we get: W = 10.
Substituting this value of W back into the equation L = W + 40, we get: L = 10 + 40 = 50.
So, the length of the rectangular field is 50 m and the width is 10 m.
The area of the rectangular field is given by the formula: A = L * W = 50 * 10 = 500 m^2.
The area of a square is given by the formula: A = side^2.
Setting up an equation to find the side length of the square, we get: side^2 = 500.
Taking the square root of both sides, we get: side = sqrt(500) = 10sqrt(5).
Therefore, the sides of the square field whose area is equal to the rectangular field are 10sqrt(5) m.
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