Question

Mrs. Norman wants to make square cookies. The length of each side will be a whole number ( in millimeters)choose all of the possible areas for the cookies.A. 300B. 400C. 64D. 80E. 255F. 1

Answer 1

Since the area of the square is express as :

`\text{ Area of Square = Side}^2`

Mrs. Norman want the meausrement of the side of the cookies in the whole number :

(A) 300

Subtitute the value of the 300 in the expression of area

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=300 \\ \text{Side}=\sqrt[]{300} \\ \text{Side }=17.32 \\ \text{Which is not a whole number} \end{gathered}`

(B) 400

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=400 \\ \text{Side}=\sqrt[]{400} \\ \text{Side }=20\text{ } \\ \text{Which is a whole number} \end{gathered}`

So, the possible area coud be 400 milimeter square

(C) 64

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=64 \\ \text{Side}=\sqrt[]{64} \\ \text{Side }=8\text{ } \\ \text{Which is a whole number} \end{gathered}`

So, the possible area could be 64 milimeter square

(D). 80

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=80 \\ \text{Side}=\sqrt[]{80} \\ \text{Side }=8.94 \\ \text{Which is not a whole number} \end{gathered}`

SO, the possible area could not be 80 milimeter square

(E) 255

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=255 \\ \text{Side}=\sqrt[]{255} \\ \text{Side }=15.9 \\ \text{Which is a not a whole number} \end{gathered}`

So, the possible area could not be 255 milimeter square

(F). 1

`\begin{gathered} \text{ Area of Square = Side}^2 \\ \text{Side}^2=Area\text{ of Square cookies} \\ \text{Side}^2=1 \\ \text{Side}=\sqrt[]{1} \\ \text{Side }=1 \\ \text{Which is a whole number} \end{gathered}`

So, the possible area could be 1 milimeter square

Answer :

Possible area for the square cookies area :

B) 400

C) 64

F) 1