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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.

Sagot :

The perimeter P of the given rectangle is

[tex]\begin{gathered} P_{\text{rectangle}}=5+5+7+7 \\ P_{\text{rectangle}}=24\text{ cm} \end{gathered}[/tex]

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

[tex]P_{\text{square}}=4\times L[/tex]

since

[tex]P_{\text{square}}=P_{\text{rectangle}}[/tex]

we get

[tex]24=4\times L[/tex]

then, L is given by

[tex]\begin{gathered} L=\frac{24}{4} \\ L=6\operatorname{cm} \end{gathered}[/tex]

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

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