Question

Which is better? A length of 9 and a perimeter of 22 or A length of 5 and a perimeter of 20?

Answer 1

We are to choose between a Cheez-it's that cover a rectangle with;

(i) A length of 9 and a perimeter of 22,

(ii) A length of 5 and a perimeter of 20.

The prefer one would be the one with a greater area.

`\begin{gathered} \text{Length = 9 units} \\ \text{Perimeter = 22 units} \\ P\text{ = 2(L + W)}=22\text{ } \\ 2(9\text{ + w) = 22} \\ (2(9+w))/(2)=\text{ }(22)/(2) \\ 9+w\text{ = 11} \\ w\text{ = 11-9} \\ w\text{ = 2 units} \end{gathered}`

The area of this rectangle is;

`\begin{gathered} A=LXW\text{ } \\ A\text{ =9X2} \\ A=18unit^2 \end{gathered}`

`\begin{gathered} \text{Length }=\text{ 5 units} \\ \text{Perimeter = 20 units} \\ P\text{ = 2(L + W) = 20} \\ 2(5\text{ + w) = 20} \\ (2(5+w))/(2)=\text{ }(20)/(2) \\ 5\text{ + w = }10 \\ w=10-5 \\ w\text{ = 5 units} \end{gathered}`

The area of this rectangle is;

`\begin{gathered} A\text{ = L x W} \\ A\text{ = 5 x 5} \\ A=25units^2 \end{gathered}`

CONCLUSION:

Since the area of a rectangle of length of 5 and a perimeter of 20 is greater than that of a length of 9 and a perimeter of 22.

The preferred is the Cheez-it's that covers a rectangle of a length of 5 and a perimeter of 22.