A rectangle has the same area as another , whose length is 6 m and breadth is 4 m less it has also the same area as the third whose length is 8 m more and breadth 5 m less find the length and breadth of the original rectangle
Answers
Answer:
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)