If the perimeter of a rectangle is 138 meters and the difference between the length and the breadth is 7 meters. what is the area of the rectangle
Answers
Given :
- Perimeter of rectangle = 138 m
- Difference between the length and the breadth of rectangle = 7 m
To find :
- Area of rectangle
Concept :
Formula of perimeter of rectangle :-
- Perimeter = 2(l + b)
Formula to calculate area of rectangle :-
- Area = l × b
where,
- l = length of the rectangle
- b = breadth of the rectangle
Solution :
Let,
- length of the rectangle = x meter
- Breadth of the rectangle = y meter
According to the condition given in he question,
→ Difference between length and breadth = 7 m
→ x - y = 7 -------(1)
Using formula,
Perimeter of rectangle = 2(l + b)
Substituting the given values,
→ 138 = 2(x + y)
→ Transpoing 2 to the other side.
→ 138 ÷ 2 = x + y
→ 69 = x + y
→ x + y = 69 ------(2)
Solving eqn. (1) and (2).
⠀⠀⠀⠀⠀⠀x + y = 69
⠀⠀⠀⠀⠀⠀x - y = 7
⠀⠀⠀⠀⠀__________
⠀⠀⠀⠀⠀⠀2x⠀ = 76
⠀⠀⠀⠀⠀__________
→ 2x = 76
→ x = 76 ÷ 2
→ x = 38
The value of x = 38.
Substitute the value of x in (1).
→ x - y = 7
→ 38 - y = 7
→ - y = 7 - 38
→ - y = - 31
→ y = 31
The value of y = 31.
Substitute the value of x and y in the length and breadth of the rectangle.
- Length of the rectangle = x = 38 m
- Breadth of the rectangle = y = 31 m
Using formula,
Area of rectangle = l × b
Substituting the given values,
→ Area = 38 × 31
→ Area = 1,178
★ Area of the rectangle = 1,178 m².
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Verification :-
For verifying our answer we will find the perimeter of the rectangle if the resultant value will be equal to the value mention in the question then the answer is right.
- Length = 38 m
- Breadth = 31 m
Perimeter = 2(l + b)
→ Perimeter = 2(38 + 31)
→ Perimeter = 2(69)
→ Perimeter = 138
Perimeter of the rectangle = 138 m.
Hence, verified.