Question

The perimeter of a rectangle is 200 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 900 feet.

ANSWER: The length (in feet) of a side is in the interval ___ or in the interval ____

Answer 1

Need my interpretation??

Answer 2

yes!!! very bad

Answer 3

area = W*L < =900

Answer 4

from the area, you have 2 numbers, W and L , maximum product of them is 900. Now consider what happens
900 = 1*900 --> the W =1 and L=900. However 1+900 =901 , too much bigger than W+L =100 above. Got me so far??

Answer 5

900 = 2*450 also. The same reason of above, we reject this result because 2+450=452 \(\neg\)100

Answer 6

how bout 900=10*90 ?? which gives us the W =10 and the L = 90
Okie dokie, If W =10, L =90, then W+L =10+90= 100 and W*L=900
so, the first solution is 10 for width and 90 for length.
got me so far??

Answer 7

yes yes yes

Answer 8

ok, the leftover is your duty. hihihi I don't have any words to interpret more. :)

Answer 9

wait so if those are your solutions than how do you write those in interval notation? That's the part that also stumps me

Answer 10

Actually, if the condition of perimeter is lesser or equal 100, then you have interval. In this case, you have just = 100, you don't have interval, just exactly 1 solution. Hopefully you missed the "lesser" part on it.

Answer 11

*200, not100

Answer 12

the question is asking me for two intervals

Answer 13

with two blanks

Answer 14

The length in feet of a side is the interval ___ or in the interval ____

Answer 15

I know!! but the condition of the perimeter must be "lesser or equal 200"
not just "is 200

Answer 16

right right

Answer 17

so would that make one of them (-inf,200]

Answer 18

for example, if I have W =45, L = 20, I still have 45*20=900 but 45+20 =65 not 100

Answer 19

help me please @tkhunny

Answer 20

Just thinking about the Area

\(0 < Length < 900\)

\(0 < Width < 900\)

Now to consider the perimeter.

\(0 < Length < 100\)

\(0 < Width < 100\)

Now the relationship between the two.

L*W < 900

2L+2W = 200 ==> 2L + 1800/L = 200 ==> 2L^2 - 200L + 1800 = 0

L = 90 or 10 <== Are these the limits?

Try it out.

L = 85, then W = 900/85 = 4.615 and 2*85 + 2*10.588 = 191.176 -- Hmmm... What are we missing?

gtg

Answer 21

That's more professional than my interpreting. However, the condition of the perimeter should be changed to < = 200. :)

Answer 22

Okay I understand how to solve it now I just don't know how to write the answer down!

Answer 23

Thank you for that step by step though from both of you that helped a lot

Answer 24

Yup. Go OOOPS! It hit me about an hour later that I was using

Area = 900 and Perimeter < 200 instead of the other way around.

Answer 25

Can somebody please tell me how to write the answer in interval notation please