Please help me guys.BEST ANSWER WILL BE BRAINLIEST. "The perimeter of a rectangular plot is 120m. The lenght of the plot is decreased by 5m and breadth is increased by 5m,then the area is increased by 75 sq.m .Find the dimensions of the plot."
Answers
It was given that
2l+2b=120m
l+b=60
l=60-b
after---
(l-5)(b+5)=75sqm
(60-b-5)(b+5)=75
(55-b)(b+5)=75
(55b-b^2-5b+275)=75
b^2-50b-200
solve it
Answer:
40 m, 20 m
Step-by-step explanation:
Let the length and breadth of rectangular plot be l and b.
(i)
Given, Perimeter is 120 m.
⇒ 2(l + b) = 120
⇒ l + b = 60
∴ Area of rectangular plot = lb
(ii)
Length is decreased by 5 m and breadth is increased by 5 m.
Area = (l - 5) * (b + 5)
(iii)
Area is increased by 75 m.
⇒ (l - 5) * (b + 5) = lb + 75
⇒ lb + 5l - 5b - 25 = lb + 75
⇒ 5(l - b) = 100
⇒ l - b = 20
On solving (i) & (iii), we get
⇒ l + b = 60
⇒ l - b = 20
---------------
2l = 80
l = 40.
Substitute l = 40 in (i), we get
⇒ l + b = 60
⇒ 40 + b = 60
⇒ b = 20.
Therefore, dimensions of the plot are:
Length = 40 m.
Breadth = 20 m.
Hope it helps!