Question

1. mountain view middle school students work on square desktops. the area of the square desk surface is 4 square feet. what is the length of each side of the desktop?
2. the volume of a cube is 64 cubic feet. what are the lengths of the sides of the cube?
3. a square garden has an area of 144 square feet. how many yards of fence will it take to enclose the garden?

Explanation:

Step1: Recall area formula for square

For a square with side length $s$, the area $A = s^2$. Given $A = 4$ square - feet, we solve for $s$.
\[s=\sqrt{A}\]
\[s=\sqrt{4}=2\] feet

Step2: Recall volume formula for cube

For a cube with side length $a$, the volume $V=a^3$. Given $V = 64$ cubic - feet, we solve for $a$.
\[a=\sqrt[3]{V}\]
\[a=\sqrt[3]{64}=4\] feet

Step3: Find side length of square garden and perimeter in yards

First, for a square garden with area $A = 144$ square - feet, using $A = s^2$, we find the side length $s$.
\[s=\sqrt{A}=\sqrt{144}=12\] feet
The perimeter $P$ of a square is $P = 4s$. So $P=4\times12 = 48$ feet.
Since 1 yard = 3 feet, to convert feet to yards, we divide by 3.
The length of fence in yards is $\frac{48}{3}=16$ yards.

Answer:

1. 2 feet
2. 4 feet
3. 16 yards