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The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq. m. The length of the larger side of the rectangle is :
- a)70 m
- b)60 m
- c)40 m
- d)50 m
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The perimeter of a rectangle and a square are 160 m each. The area of ...
Given,
Perimeter of rectangle = 160m = 2(length + breadth)
Length + breadth = 80
Perimeter of rectangle = 160m = 2(length + breadth)
Length + breadth = 80
Perimeter of square = 160m = 4 × side of square
Side of square = 40m
Area of square = 40 × 40 = 1600 sq m
Side of square = 40m
Area of square = 40 × 40 = 1600 sq m
Given,
Area of rectangle = 1600 – 100 = 1500 sq.cm
Area of rectangle = length × breadth
⇒ Length × breadth = 1500
Solving equations,
⇒ Length + 1500/length = 80
⇒ Length2 + 1500 – 80 length = 0
⇒ Length = 50 or 30
∴ Length of rectangle is 50 cm.
Area of rectangle = 1600 – 100 = 1500 sq.cm
Area of rectangle = length × breadth
⇒ Length × breadth = 1500
Solving equations,
⇒ Length + 1500/length = 80
⇒ Length2 + 1500 – 80 length = 0
⇒ Length = 50 or 30
∴ Length of rectangle is 50 cm.
Most Upvoted Answer
The perimeter of a rectangle and a square are 160 m each. The area of ...
Given information:
Perimeter of rectangle = 160 m
Perimeter of square = 160 m
Area of rectangle < area="" of="" square="" by="" 100="" sq.="" />
To find:
Length of the larger side of the rectangle
Let's assume:
Length of rectangle = L
Width of rectangle = W
Side of square = S
Perimeter of rectangle:
2(L + W) = 160
L + W = 80
Perimeter of square:
4S = 160
S = 40
Area of rectangle:
L * W = Area of square - 100
L * W = S^2 - 100
L * W = 40^2 - 100
L * W = 1600 - 100
L * W = 1500
Now, we have two equations:
L + W = 80
L * W = 1500
Solving the equations:
Let's express L in terms of W using the first equation.
L = 80 - W
Substituting this value of L in the second equation:
(80 - W) * W = 1500
80W - W^2 = 1500
W^2 - 80W + 1500 = 0
Now, we can solve this quadratic equation to find the values of W.
By factorizing the equation, we get:
(W - 50)(W - 30) = 0
Setting each factor equal to zero:
W - 50 = 0 or W - 30 = 0
W = 50 or W = 30
Since the length cannot be smaller than the width, we take W = 50.
Substituting this value of W in the first equation:
L + 50 = 80
L = 80 - 50
L = 30
Therefore, the larger side of the rectangle is 50 m (option D).
Perimeter of rectangle = 160 m
Perimeter of square = 160 m
Area of rectangle < area="" of="" square="" by="" 100="" sq.="" />
To find:
Length of the larger side of the rectangle
Let's assume:
Length of rectangle = L
Width of rectangle = W
Side of square = S
Perimeter of rectangle:
2(L + W) = 160
L + W = 80
Perimeter of square:
4S = 160
S = 40
Area of rectangle:
L * W = Area of square - 100
L * W = S^2 - 100
L * W = 40^2 - 100
L * W = 1600 - 100
L * W = 1500
Now, we have two equations:
L + W = 80
L * W = 1500
Solving the equations:
Let's express L in terms of W using the first equation.
L = 80 - W
Substituting this value of L in the second equation:
(80 - W) * W = 1500
80W - W^2 = 1500
W^2 - 80W + 1500 = 0
Now, we can solve this quadratic equation to find the values of W.
By factorizing the equation, we get:
(W - 50)(W - 30) = 0
Setting each factor equal to zero:
W - 50 = 0 or W - 30 = 0
W = 50 or W = 30
Since the length cannot be smaller than the width, we take W = 50.
Substituting this value of W in the first equation:
L + 50 = 80
L = 80 - 50
L = 30
Therefore, the larger side of the rectangle is 50 m (option D).
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The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq. m. The length of the larger side of the rectangle is :a)70 mb)60 mc)40 md)50 mCorrect answer is option 'D'. Can you explain this answer?
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