The perimeter of a rectangle is 36 centimetres.
(a) What is the sum of its length and breadth ?
(b) If the area of this rectangle is 80 square centimetres, find its length and breadth.
Answers
Step-by-step explanation:
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Answer :
Perimeter = 2(l+b) = 36
=> l+ b = 18.
You can find your answer simply by checking multiplication of each set of possible numbers from 1 to 18.
But for larger or complex problems you can use method of maxima and minima.
=> b = 18 - l
Let A be the area of rectangle.
A = l×b = l×(18-l) = 18l - l^2
Taking derivative both sides w.r.t l
=> dA/dl = 18 - 2l —(i)
To find maxima or minima,
18 - 2l = 0
=> 2l = 18
=> l = 9
Tking derievative of equation (i)
d^2A/dl^2 = -2
which is negative at l=9.
So, A will be maximum at l = 9.
Max Area = 9*(18-9) = 81
1.all sqaures are rectangles also
2.a rectangle has maximum area when it is a square.)
and its minima is not defined.
As for area to be minimum, l -> 0 and we cannot define what exactly is value of l and thus there is no definite value of minimum area.
At l = 0, It becomes a line and cannot be said a rectangle.
As we need whole numbers, so, here the possible minimum area is when l = 1
Minimum Area = 1×17 = 17.