Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find
its length and breadth.
Answers
Answer:
length=20m and breadth =20m
Step-by-step explanation:
2(l+b)=80
=>l+b=40
therefore l+b=40 ..this is equation no.1
l×b=400
=>b=400/l
substituting the value of b in equation no. 1 ...we get
l+400/l=40
=>l²+400=40l
=>l²-40l+400=0
l²-(20+20)l+400=0
l²-20l-20l+400=0
l(l-20)-20(l-20)=0
(l-20)(l-20)=0
therefore,either (l-20)=0
l=20m
or(l-20)
l=20m
therefore the length is 20 m and the breadth is also 20m.
But it is not possible to make a rectangular park...because the length and breadth are the same ...so its a square
★Given :
- Perimeter = 80m
- Area = 400m²
★To find :
- Is it possible to design a rectangular park with given info.
- Length and breadth, if possible.
★Solution :
Let length and breadth of the park be l and b.
Using the formula,
→Perimeter = 2 (l + b)
Given that perimeter = 80m
→2(l+b)= 80
→l + b = 40
→b = 40 - l___(1)
We know,
→Area = l×b
Substituting the value of b from (1) in the area,
→Area = l (40 - l)
→40 l - l² = 400
→l² - 40 l + 400 = 0___(2)
→l² - 20l - 20l +400 = 0
→l(l-20) - 20(l - 20) = 0
→(l-20)(l-20) = 0
→l = 20m
Comparing equation (2) with ax² + bx + c = 0,
→a = 1, b = -40, c = 400
We know,
→Discriminant = b² - 4ac
Substituting the values,
→(-40)² - 4 × 400(1)
→1600 - 1600 = 0
∴b² - 4ac = 0
Therefore, this equation has equal real roots.
Hence, this situation is possible.
We have,
- b = 40 - l
Substituting the value of l,
→b = 40 - 20
→20 m.
Therefore,the length and breadth are 20m,20m respectively.