Question

a rectangle has same area as another, whose length is 6m more and breadth is 4m less it has also same as third whose length is 8m more and breadth is 5m less​

Answer 1

The dimensions of the rectangle are 24 m by 20 m.

Step-by-step explanation:

Let us assume that the length of the rectangle is L and breadth is B.

Given that the rectangle has the same area as another, whose length is 6 m more and breadth is 4 m less.

Hence, (L + 6)(B - 4) = LB

⇒ 6B - 4L = 24 ........ (1)

⇒ 30B - 20L = 120 ........ (2)

Again, same as third one whose length is 8 m more and breadth is 5 m less.

So, (L + 8)(B - 5) = LB

⇒ 8B - 5L = 40 .......(3)

⇒ 32B - 20L = 160 .......... (4)

Now, solving equations (2) and (4) we get, 2B = 40

⇒ B = 20 m

And from equation (1) we get, 4L = 6B - 24 = 120 - 24 = 96

⇒ L = 24 m

So, the dimensions of the rectangle are 24 m by 20 m. (Answer)