Question

has the same area as another, whose length is 6 m more and breadth
It has also the same area as the third, whose length is 8 m more and
less. Find the length and breadth of the original rectangle.
bility that 1) A rectangle has the
Following is 4 m less. It has
breadth 5 m less.
32​

Answer 1

Answer:

Length of original rectangle is 24 m and width of original rectangle is 20 m.

Step-by-step explanation:

1. Let length of original rectangle = L

Width of original rectangle = B

Area of first rectangle (A_{1}A

1

) = L× B

2. Now from given question

length of second rectangle = L +6

Width of second rectangle = B - 4

Area of second rectangle (A_{2}A

2

) = (L + 6)× (B -4)

3. Also for third rectangle

length of third rectangle = L + 8

Width of third rectangle = B - 5

Area of third rectangle(A_{3}A

3

) = (L + 8)× (B -5)

4. Now given that

A_{1} = A_{2} = A_{3}A

1

=A

2

=A

3

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

5. Take equation 1) can be written as

L× B = (L + 6)× (B -4)

LB = LB - 4L + 6B - 24

4L - 6B = - 24 ...2)

6. Again equation 1) can be written as

L× B = (L + 8)× (B -5)

LB = LB - 5L + 8B - 40

5L - 8B = - 40 ...3)

7. On solving equation 2) and equation 3)

We get original length (L) = 24 (m)

and original width (B) = 20 (m)