A square with a perimeter of $137$ units is the image of a square that was dilated by a scale factor of $4$ . Find the perimeter of the preimage, the original square, before its dilation. Round your answer to the nearest tenth, if necessary. $\newline$ Answer: units

View step-by-step help

Home

Math Problems

Algebra 1

Scale drawings: word problems

Full solution

Q. A square with a perimeter of

137

units is the image of a square that was dilated by a scale factor of

4

. Find the perimeter of the preimage, the original square, before its dilation. Round your answer to the nearest tenth, if necessary.

\newline

Answer: units

Calculate Side Length: First, we need to understand that the perimeter of a square is four times the length of one side. Since the perimeter of the dilated square is $137$ units, we can find the length of one side of the dilated square by dividing the perimeter by $4$ . $\newline$ Calculation: Side length of dilated square = $137$ units $/$ $4$
Find Original Side Length: Now, we divide $137$ by $4$ to find the length of one side of the dilated square. $\newline$ Calculation: $137 / 4 = 34.25$ units
Calculate Original Perimeter: Next, we use the scale factor to find the length of one side of the original square. The scale factor is given as $4$ , which means the side of the dilated square is $4$ times longer than the side of the original square. $\newline$ Calculation: Side length of original square = Side length of dilated square / Scale factor = $34.25$ units / $4$
Final Answer: We calculate the side length of the original square. $\newline$ Calculation: $34.25 / 4 = 8.5625$ units
Final Answer: We calculate the side length of the original square. $\newline$ Calculation: $34.25 / 4 = 8.5625$ unitsTo find the perimeter of the original square, we multiply the length of one side by $4$ . $\newline$ Calculation: Perimeter of original square = $4 \times$ Side length of original square = $4 \times 8.5625$ units
Final Answer: We calculate the side length of the original square. $\newline$ Calculation: $34.25 / 4 = 8.5625$ unitsTo find the perimeter of the original square, we multiply the length of one side by $4$ . $\newline$ Calculation: Perimeter of original square = $4 \times$ Side length of original square = $4 \times 8.5625$ unitsWe perform the multiplication to find the perimeter of the original square. $\newline$ Calculation: $4 \times 8.5625 = 34.25$ units
Final Answer: We calculate the side length of the original square. $\newline$ Calculation: $34.25 / 4 = 8.5625$ unitsTo find the perimeter of the original square, we multiply the length of one side by $4$ . $\newline$ Calculation: Perimeter of original square = $4 \times$ Side length of original square = $4 \times 8.5625$ unitsWe perform the multiplication to find the perimeter of the original square. $\newline$ Calculation: $4 \times 8.5625 = 34.25$ unitsSince the problem asks for the perimeter of the original square before dilation and rounding to the nearest tenth is not necessary because our answer is already in a tenth, we have our final answer. $\newline$ Calculation: The perimeter of the original square is $34.25$ units.