Question

A rectangle has the same area as another whose length is 6 m more and breadth 4less.it has also the same area as the third whose length is 8 m more and breadth 5m less.find length and breadth of a rectangle​

Answer 1

If the area of a rectangle is equal to the second and the third rectangle then the length and breadth of the original rectangle are 24 m and 20 m respectively.

Step-by-step explanation:

Let the length and breadth of the original rectangle be “l” & “b” respectively.

It is given that, the area of the original rectangle is equal to the area of another rectangle with length 6 m more and breadth 4 m less, so we can write the eq. as,

lb = (l+6)(b-4)  

⇒ lb = lb – 4l + 6b – 24

⇒ – 4l + 6b – 24 = 0 …… (i)

Also given that, the area of the original rectangle is equal to the area of the third rectangle with length 8 m more and breadth 5 m less, so we can write the eq. as,

lb = (l+8)(b-5)  

⇒ lb = lb – 5l + 8b – 40

⇒ – 5l + 8b – 40 = 0 …… (ii)

Now, multiplying eq. (i) with 5 and eq. (ii) with 4 and then subtracting bothe equations, we get

-20l + 30b -120 = 0

-20l +32b – 160 = 0

+      -         +

--------------------------------

2b = 40

---------------------------------

∴ b = 20 m

Substituting b = 20 m in eq. (i), we get

– 4l + (6*20) – 24 = 0

⇒ - 4l = -96

⇒ l = 24 m

Thus, the length of the rectangle is 24 m and breadth is 20 m.

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