the length of the rectangle is 5 metres less than twice the breadth . if the perimeter is 50 meters, find the length and breadth of the rectangle
Answers
Step-by-step explanation:
Let the breadth of the rectangle be x meter.
The length of a rectangle is 5 meters less than twice the breadth. So, twice the breadth is 2*x = 2x, and 5 meters less than twice the breadth is 2x-5.
Therefore, the length of the rectangle = (2x-5)m
Formula for perimeter of a rectangle = 2(l + b)
Perimeter of the rectangle = 50m = 2(l +b)
Therefore,
2(l + b) = 2(2x-5 + x) {Substituting the values of l and b}
=50 = 2(3x-5) = 6x-10
=6x = 50 + 10 = 60
=x = 60/6 = 10m
Therefore,
Breadth = x = 10m
Length = 2x-5 = 2*10-5 = 20-5 = 15m
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Given :
• Length of the rectangle is 5 metre less than twice the breadth
• Perimeter of the rectangle = 50 metres
To find :
• Length and breadth of the rectangle
Solution :
Let us assume the breadth of the rectangle as x metre and length as 2x - 5 metre
Using formula,
• Perimeter of rectangle = 2(l + b)
where,
• l denotes the length of the rectangle
• b denotes the breadth of the rectangle
Substituting the given values :-
→ 50 = 2(2x - 5 + x)
→ 50 ÷ 2 = 2x - 5 + x
→ 25 = 3x - 5
→ 25 + 5 = 3x
→ 30 = 3x
→ 30 ÷ 3 = x
→ 10 = x
→ The value of x = 10
Substitute the value of x in the dimensions of rectangle which we've let :-
→ Length = 2x - 5 = 2(10) - 5 = 20 - 5 = 15 m
→ Breadth = x = 10 m
Therefore, the dimensions of rectangle are :-
- Length = 15 m
- Breadth = 10 m