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rectangle has the same area as another, whose length is 6 m more and breadth
A rectangle ba
is 4 m less. It
m less. It has also the same area as the third, whose length is 8 m more and
dth 5 m less. Find the length and breadth of the original rectangle.
Answers
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 both the 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 original rectangle is 24 m and breadth is 20 m.
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