Question

A wire was bent into the shape of a rectangle with width 5 and length 7. If the same wire is bent into the shape of a square, what is the length of a side of the square? 3 B 6 24

Answer 1

If the wire was bent into a rectangle with dimensions 5 and 7, the perimeter of this rectangle corresponds to the length of the wire:

$\begin{gathered} \text{Perimeter}=2\cdot5+2\cdot7 \\ \text{Perimeter}=10+14 \\ \text{Perimeter}=24 \end{gathered}$

So if we use the same wire to make a square with side equal x, the perimeter of this square is 4x, so:

$\begin{gathered} \text{Perimeter}=4x \\ 24=4x \\ x=\frac{24}{4} \\ x=6 \end{gathered}$

So the side of the square is 6 units, therefore the correct option is B.