is it possible to design a rectangular hall of perimeter 100 and area 600m^2 . if so find its dimensions.
Answers
Step-by-step explanation:
So, the given quadratic equation has equal roots and hence it is possible to design a rectangular park. Hence, length of the rectangular park (x) = 20 m and breadth = (40 – x) m = 40 – 20 = 20 m.
Is it possible to design a rectangular Mango grove whose length is twice its breadth and the area is 800 m2? ... So, the given quadratic equation has real roots (∵ D > 0) and hence it is possible to design rectangular mango grove.
Let the length be l m and the breadth be b m.
Then the area would be lb=400
Perimeter would be 2(l+b)=80
lb=400
⇒2(l+b)=80
⇒l+b=40
∴b=40−l --(1)
Substituting (1) in Area, we get
⇒l(40−l)=400
⇒40l−l
2
=400
⇒l
2
−40l+400=0
⇒(l−20)(l−20)=0
∴l=20
has equal roots, so it is possible to design the rectangle of given parameters.
⇒b=40−20=20
We now know that the length of the park is 20 m and the breadth of the park is also 20 m.
Answer:
dimensions of that rectangle hall are l = 30 b = 20
Step-by-step explanation:
In a rectangular hall,
Let length be denoted by l and breath be denoted by b
⇒ Perimeter is 100 m
Perimeter = 2 (l + b) = 100
l + b = 50________(1)
⇒ Area is 600 m²
Area = lb = 600 _________(2)
Consider (1)
l = 50 - b
Substitute l in (2)
(50 - b) (b) = 50b - b² = 600
b² - 50 b + 600 = 0
b² - 20b - 30b + 600 = 0
b(b - 20) - 30 (b - 20) = 0
(b-20)(b-30) = 0
b = 20 or 30
If b = 20
l = 50 - 20
l = 30
If b = 30
l = 50 - 30
l = 20 (This case is not possible because l cannot be less than b)