The Length of a rectangle exceeds its breadth by 4 cm. If Length and Breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle. Find the length and breadth of the given rectangle.
Answers
Step-by-step explanation:
Given :-
The Length of a rectangle exceeds its breadth by 4 cm. If Length and Breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.
To find :-
Find the length and breadth of the given rectangle?
Solution :-
Let the breadth of the rectangle be X cm
Then , the length of the rectangle
= Breadth + 4 cm
= (X + 4) cm
We know that
Area of a rectangle = lb sq.units
Area of the given rectangle
= (X+4) × X cm²
=> (X×X) +(4×X)
=> X²+4X cm²
Area of the given rectangle =(X²+4X) cm²---(1)
If the length is increased by 3 cm then
The length of the new rectangle
= X+4+3
= (X+7) cm
If the breadth is Increased by 3 cm then
The breadth of the new rectangle
= (X+3) cm
Area of the new rectangle
= (X+7)×(X+3) cm²
=> X×(X+3) + 7×(X+3)
=> X²+3X+7X+21
=> X²+10X+21 cm²
Area of the new rectangle=(X²+10X+21) cm²---(2)
Given that
If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.
=> Area of the new rectangle = Area of the given rectangle + 81 cm²
=> X²+10X+21 = X²+4X+81
=> 10X+21 = 4X+81
=> 10X-4X = 81-21
=> 6X = 60
=> X = 60/6
=> X = 10 cm
Therefore, Breadth = 10 cm
Length = X+4 = 10+4 = 14 cm
Answer:-
The length of the given rectangle = 14 cm
The breadth of the given rectangle = 10 cm
Check :-
Length = 14 cm
Breadth = 10 cm
Length = 10+4 cm
Length = Breadth + 4 cm
Area of the rectangle = 14×10 = 140 cm²
If the length and breadth is Increased by 3 cm each then they will be 14+3 =17 cm
and 10+3 = 13 cm
Area of the new rectangle = 17×13 = 221 cm²
New area = 221 cm²
=> New Area = 140+81
=> New Area = Area of the given rectangle +
81 cm²
If length and breadth are each increased by 3 cm, the area of the new rectangle will be 81 cm² more than that of the given rectangle.
Verified the given relations in the given problem.
Used formulae:-
- Area of a rectangle = lb sq.units
- l = length of a rectangle
- b = breadth of a rectangle