Question

A rectangle has the same area as another, whose length is 6 mntore and breadth
is 4 m less. It has also the same area as the third, whose length is m more and
breadth 5 m less. Find the length and breadth of the original rectangle​

Answer 1

Let length of original rectangle = L

Width of original rectangle = B

Area of first rectangle ($A_1$) = L× B

Now from given question

Length of second rectangle = L + 6

Width of second rectangle = B - 4

Area of second rectangle ($A_2$) = (L + 6) × (B - 4)

For third rectangle :-

Length of third rectangle = L + 8

Width of third rectangle = B - 5

Area of third rectangle($A_3$) = (L + 8) × (B - 5)

Now given that :-

L× B = (L + 6) × (B - 4) = (L + 8) × (B - 5)______(1)

(1) can be written as

L× B = (L + 6) × (B - 4)

LB = LB - 4L + 6B - 24

4L - 6B = - 24________(2)

(2) can be written as

L× B = (L + 8)× (B -5)

LB = LB - 5L + 8B - 40

5L - 8B = - 40________(3)

On solving equation (2) and equation (3)

Original length (L) = 24 m

Original width (B) = 20 m