The length of a rectangle is twice its breadth. If the ratio of the perimeter of the rectangle and its area is 1:2, find the dimensions of the rectangle.
Answers
Answer:
Solution
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Let the breadth of the rectangle is b cm.
So, the length of the rectangle is 2b cm.
We know that the perimeter of rectangle is
=2(l+b)
Since, perimeter of rectangle is 120 cm.
Therefore,
6b=120
b=20 cm
And l=40 cm
So, the area of rectangle is
=20×40=800 cm2
Hence, the length is 40 cm, breadth is 20 cm and area is 800 cm2.
Answer:
Given:-
the length of a rectangle is twice its breadth
the ratio of the perimeter of the rectangle and its area is 1:2
To find :-
The dimensions of the rectangle i.e length and breadth of the rectangle.
Solution :-
As per the first given statement,
the length of a rectangle is twice its breadth,
Let the breadth of the rectangle= x cm
Then, the length of the rectangle = 2x cm
Perimeter and area are in the ratio 1:2,
Perimeter :Area = 1:2
=
Formulaes for perimeter and area of rectangle,
Perimeter = 2 (l+b)
Area = L × B
=
Plug the values,
=
=
=
Cross multiplying the terms,
2 (6x) = 1 × 2x²
12x = 2x²
•°• 2x² = 12x
•°• 2x² - 12x = 0
•°• 2x (x - 6) = 0
2x = 0 OR x - 6 = 0
x = OR x = 6
x = 0 OR x = 6
Since, x = breadth = 6cm
Substitute this value of x in length,
length = 2x = 2 × 6 = 12 cm
As given in the question,
For first case :-
the length of a rectangle is twice its breadth
Length = 2x = 2 × 6 = 12cm
Breadth = x = 6cm
12 = twice of 6 i.e, length of the rectangle is twice the breadth.
Hence the first condition is satisfied.
For second case :-
the ratio of the perimeter of the rectangle and its area is 1:2
Perimeter of the rectangle = 2(l+b)
Perimeter = 2 (12 + 6)
Perimeter = 2 (18)
Area of the rectangle = l × b
Area = 12 × 6
Ratio of perimeter and area = 1:2
Perimeter : Area = 1:2
=
Dividing LHS by 36,
=
LHS = RHS.
Hence verified!