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.
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Answer :-
The length of Rectangle = 14cm.
Breadth of Rectangle = 10cm.
Step-by-step explanation:
To Find :-
- The length and breadth of rectangle.
★ Solution
Given the,
The length of Rectangle exceeds it's breadth by 4m.
Assumption
Let us assume the breadth of rectangle as (x) cm and the length of rectangle as (x + 4)cm .
Also given,
Length and breadth are increased by 3cm .
∴ Length = (x + 4) + 3 = (x + 7)m ; Breadth = (x + 3)m .
We know,
Area of rectangle = lb sq. units,
Where,
- l = Length
- b = Breadth
According the question,
⇒ (x + 7) (x + 3) = 81 + (x) (x + 4)
⇒ x² + 7x + 3x + 21 = 81 + x² + 4x
⇒ x² + 10x + 21 = 81 + x² + 4x
⇒ 10x + 21 = 81 + 4x
⇒ 10x - 4x = 81 - 21
⇒ 6x = 60
⇒ x = 60/6
⇒ x = 60
We got, The value of x is 60.
Now, The length and breadth of rectangle :-
⇒ Length = (x + 4) = (10 + 4) = 14m
⇒ Breadth = (x) = 10m
∴ The length and breadth of rectangle is 14m and 10m.
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