5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m?? If so, find
its length and breadth.
Who ever answers this I will mark him/her brainliest.
Answers
let length be x and breadth be y
perimeter of the rectangle = 80 m
=> 2 ( length + breadth ) = 80 m
=> x + y = 40 m..........(1)
area of the rectangle = 400 m²
=> xy. = 400 m²
=> x = 400/y
from eq.1.
400/y + y. = 40
400 + y² = 40y
y² - 40y + 400 = 0
(y - 20)(y - 20) = 0
therefore y = 20 m
then x = 400/20 = 20m
therefore length = breadth = 20 m
ANSWER:
- Rectangle will not be formed
GIVEN:
- Perimeter = 80 m
- Area = 400 m²
EXPLANATION:
Area of rectangle = length × breadth
Let length be l and breadth be b
l × b = 400 m²
Perimeter of rectangle = 2( length + breadth)
2( l + b) = 80 m
l + b = 40 m
l = 40 - b
Substitute l = 40 - b in l × b = 400 m²
(40 - b) × b = 400
40 b - b² = 400
b² - 40 b + 400 = 0
By splitting the middle term
b² - 20b - 20b + 400 = 0
b(b - 20) - 20(b - 20) = 0
(b - 20)(b - 20) = 0
b = 20 m
Substitute b = 20 m in l + b = 40 m
20 + l = 40
l = 20 m
Here we can see length = breadth = 20 m