An artist says that the best paintings have the same
area as their perimeter, assuming that such sizes
increases the viewer’s appreciation.
Find what sides a ‘rectangle’
must have if its area and perimeter are numerically equal.
Prepare a chart for such dimensions and mark the integral
value of dimensions in the chart.
plz tell me fast
Answers
The solutions to the given problems are as follows:
(i) Let the length and breadth of the rectangle be l and b respectively.
According to the question:
The perimeter of rectangle= The area of rectangle
⇒ 2(l + b) = l × b
⇒ 2l + 2b = lb
⇒ lb - 2l = 2b
⇒ l(b - 2) = 2b
⇒ l = 2b/(b - 2)
- This is the required relation.
- For b = 1 and b = 2, length becomes negative. So it is not possible.
- For b = 3, l = 6
So, the rectangle may have sides of 3 and 6 units if its area and perimeter are numerically equal.
(ii) Infinite combinations of sides can be possible as per the formula derived above.
- For the sake of convenience, only the chart for 3 integrals is as follows:
Length I Breadth I Perimeter
= Area
3 6 18
4 4 16
6 3 18
Answer:
et l be the length and w be the side of rectangle
according to the question
A=P
A =l*w
P=2(l+w)
A=P=>lw=2l+2w
Therefore
lw=2l+2w
lw-2l=2w
l(w-2)=2w
L=2w/w-2
now pick 'w' =3
put this in L=2w/w-2
L=2(3)/3-2
L=6/1
=6
Now put this in again inL=2w/w-2
6=2w/w-2
6w-12=2w
6w-2w=12
4w=12
w=12/4
w=3
Now Area=lw=>6×3=18
Perimeter=2l+2w
P=2×6+2×3
P=12+6
p=18
A=P=18