Question

Find the dimensions of the rectangle with area 180 square inches and smallest possible perimeter.

Answer 1

the two variables are x and z. how do I set this up in my graphing calculator to get the best answer?

Answer 2

A=x*y =180 ===> P =2(x+y) ===> P=2(x+180/x) ===> P' =2-360/x^2 ===> P' = 0 ===> x=6sqrt(5) ==> y = 180/6sqrt(5)

Answer 3

hence. from the graph at x= 6sqrt(5) is the smallest possible perimeter.

Answer 4

Make factor pairs of 1801*180
1*180
2*90
3*60
4*45
5*36
6*30
9*20
10*18
12*15

Answer 5

Smallest perimeter means a square, so the side is sqrt of 180.
\[\sqrt{180} = \sqrt{9*4*5} = 6\sqrt{5}\]

Answer 6

Try to find perimeter with each of these factor pair
1*180 ----- p=362
2*90 -------- p=184
3*60 126
4*45 98
5*36 82
6*30 72
9*20 58
10*18 56
12*15 54

As you can see, smallest possible perimeter is possible with dimensions as 12 and 15

Answer 7

okay, I see that. and if I wanted to put this as y= in my graphing calculator to sketch the graph how would I do that?