MATH SOLVE

5 months ago

Q:
# 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

Accepted Solution

A:

The length of the square that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cmExplanation:Let's call:[tex]A_{s}:Area \ of \ square \\ \\ A_{r}:Area \ of \ rectangle \\ \\ P_{s}:Perimeter \ of \ square \\ \\ P_{r}:Perimeter \ of \ rectangle[/tex]From the question, we know that:A rectangle and a square have the same perimeter.So:[tex]P_{s}=P_{r}[/tex]Moreover:The rectangle is of length 6cm and has an area of 48cm²Accordingly:[tex]For \ Rectangle: \\ \\ L:Length \\ W:Width \\ \\ A_{r}=L\times W \\ \\ 48=6W \\ \\ W=8[/tex]Also:[tex]A_{s}=s^2 \\ \\ S:Side \ of \ square[/tex]From the statement of perimeters:[tex]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}[/tex]Finally, the length of the square that has the same perimeter as the rectangle is of length 6cm and area of 48cm² is 7cmLearn more:Perimeter: