Question

A wire is first bent into the shape of a rectangle with width 5 cm and length 7 cm. Then the wire is unbent and reshaped into a square. What is the length of a side of the square.

Answer 1

The perimeter P of the given rectangle is

`\begin{gathered} P_{\text{rectangle}}=5+5+7+7 \\ P_{\text{rectangle}}=24\text{ cm} \end{gathered}`

Since the wire is the same, this perimeter must be preserved. Let L be the side of the square, then its perimeter is given by

`P_{\text{square}}=4* L`

since

`P_{\text{square}}=P_{\text{rectangle}}`

we get

`24=4* L`

then, L is given by

then, the lenght of a side of the square measure 6cm