The length of a rectangle exceeds its breadth by 9 cm. If the length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm^2 more than that of the given rectangle. Find the length and breadth of the given rectangle.
Answers
Answer:-
Length = 17 cm
Breadth = 8 cm
Solution :-
let the breadth be x
length: x+9 , breadth: x
length and breadth are incresed by 3 so,
length: x+9 +3 = x+12 ,breadth: x+3
Gn: the area of the new rectangle = 84 sq. cm
Equation:
(x+12)(x+3)= 84+ x(x+9)
x2 + 15x + 36 = 84 + x2 +9x
if we transpose x2to the opposite side then it becomes x2
x2 x2 + 15x + 36 = 84 + 9x
Now it becomes 15x+36 = 84 +9x
If we transpose 9x to the opposite side it becomes 15x +36 9x = 84
6x +36 = 84
6x = 84 36
6x= 48
x=48/6
x=8
length : 8+9 = 17
breadth= 8
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Answer:
Let the breadth of the rectangle be x cm.
Then, the length of the rectangle is (x+9) cm.
So, area of rectangle = length x breadth =x(x+9)cm
2
Now, length of new rectangle =(x+9+3) cm =(x+12) cm and
breadth of new rectangle =(x+3) cm.
So, area of new rectangle = length × breadth =(x+12)(x+3)cm
2
According to the given condition,
(x+12)(x+3)=x(x+9)+84
⇒x
2
+12x+3x+36=x
2
+9x+84
⇒15x+36=9x+84
⇒15x−9x=84−36
⇒6x=48
⇒x=8
So, breadth of the rectangle is 8 cm and length
=8+9=17 cm.