Answered

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The length of a rectangle is the same as its width. If the perimeter is 32 M what is its area?

Sagot :

The perimeter of a rectangle is calculated using the formula:

[tex]P=2(l+w)[/tex]

The question gives that the length and width of the rectangle are equal. This means that:

[tex]l=w[/tex]

Therefore, the perimeter will be calculated to be:

[tex]\begin{gathered} P=2(l+l)=2(2l) \\ P=4l \end{gathered}[/tex]

The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:

[tex]\begin{gathered} 32=4l \\ l=\frac{32}{4} \\ l=8 \end{gathered}[/tex]

Using the formula for the area:

[tex]A=l^2[/tex]

Therefore, the area will be:

[tex]\begin{gathered} A=8^2 \\ A=64\text{ m}^2 \end{gathered}[/tex]

The area is 64 square meters.

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