[tex]\huge\mathtt\purple{QUESTION}[/tex]
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2 ? If so, find its length and breadth.
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[tex]\huge\mathtt\purple{QUESTION}[/tex]
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2 ? If so, find its length and breadth.
please help me...!!
please don't delete my question..
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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−l2=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.
Verified answer
Step-by-step explanation:
a = 400m
p = 80m
400 = l×b
l = 400/b
80 = 2(l+b)
40 = 400/b +b
40b = 400+b²
b²-40b+400 = 0
b²-20b-20b+400= 0
b(b-20) -20(b-20) = 0
b= 20,20
l = 20
b= 20
yes it is possible