Question

18) The length of a rectangle is greater than the breadth by 3cm . If the length is increased by 9cm and the breadth is
reduced by 5cm ,the area remains the same. Find the dimensions of the rectangle​

Answer 1

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.

Step-by-step explanation:

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