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A picture frame has an area of $121\,\text{square centimeters}$ . Assuming it is a square, what is the perimeter of the frame? $\newline$ $\_\_\_\_\_$ centimeters

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Area and perimeter: word problems

Full solution

Q. A picture frame has an area of

121\,\text{square centimeters}

. Assuming it is a square, what is the perimeter of the frame?

\newline

\_\_\_\_\_

centimeters

Define Side Length: Let $s$ be the side length of the square. $\newline$ Since the area of a square is given by $A = s^2$ , where $s$ is the side length. $\newline$ Area of the picture frame: $121$ square centimeters. $\newline$ $121 = s^2$
Find Side Length: Solve for $s$ . $\newline$ Taking the square root of both sides to find $s$ . $\newline$ $\sqrt{121} = s$ $\newline$ $s = 11$ centimeters.
Calculate Perimeter: Calculate the perimeter of the square. $\newline$ The perimeter $P$ of a square is given by $P = 4s$ . $\newline$ Substitute $11$ for $s$ in $P = 4s$ . $\newline$ $P = 4 \times 11$ $\newline$ $P = 44$ centimeters.

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