Question

A rectangle and a square have the same perimeter. the rectangle is of length 6cm and has an area of 48cm², find the length of the square​

Answer 1

The length of the square​ that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm

Explanation:

Let's call:

$A_{s}:Area \ of \ square \\ \\ A_{r}:Area \ of \ rectangle \\ \\ P_{s}:Perimeter \ of \ square \\ \\ P_{r}:Perimeter \ of \ rectangle$

From the question, we know that:

• A rectangle and a square have the same perimeter.

So:

$P_{s}=P_{r}$

Moreover:

• The rectangle is of length 6cm and has an area of 48cm²

Accordingly:

$For \ Rectangle: \\ \\ L:Length \\ W:Width \\ \\ A_{r}=L\times W \\ \\ 48=6W \\ \\ W=8$

Also:

$A_{s}=s^2 \\ \\ S:Side \ of \ square$

From the statement of perimeters:

$P_{s}=P_{r} \\ \\ \\ But: \\ \\ P_{s}=4s \\ \\ P_{r}=2W+2L \\ \\ \\ Then: \\ \\ 4s=2W+2L \\ \\ \\ But: \ W=8 \ and \ L=6 \\ \\ 4s=2(8)+2(6) \\ \\ 4s=16+12 \\ \\ 4s=28 \\ \\ \boxed{s=7cm}$

Finally, the length of the square​ that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cm

Learn more:

Perimeter: brainly.com/question/9969486

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