The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle and choose the option which follows.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Length is 16cm and breadth is 9cm.

Length is 9cm and breadth is 16cm.

Length is 14cm and breadth is 7cm.

Length is 15cm and breadth is 8cm.

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that the length of the original rectangle is 7cm more than its breadth.
And when the length is decreased by 4 cm and the breadth is increased by 3 cm, the area remains same as before.
The area of the rectangle with length l and breadth b is as follows,

A = l × b

Now, as per the first condition, the length of the original rectangle is 7cm more than its breadth.
So, assume the breadth to be x cm.
Then its length will be (x+7) cm.
Therefore, the area of the rectangle is,

A = (x + 7) × x = x 2 + 7 x

Next, according to the second condition, the length is decreased by 4 cm and the breadth is increased by 3 cm. So, the length becomes

x + 7 − 4 = x + 3

,
and the breadth is x+3 cm. Then the area of new rectangle can be expressed as follows,

A' = (x + 3) (x + 3) = x 2 + 3 x + 3 x + 9 = x 2 + 6 x + 9

where A’ represents the area of the new rectangle.
Now, we know that the area of the original and new rectangle being same, we can setup the equation as follows,