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Polygon
C has an area of 7 square units. Jennie drew a scaled version of Polygon
C and labeled it Polygon
D. Polygon
D has an area of 28 square units.
What scale factor did Jennie use to go from Polygon
C to Polygon
D ?

Polygon $C$ has an area of $7$ square units. Jennie drew a scaled version of Polygon $C$ and labeled it Polygon $D$ . Polygon $D$ has an area of $28$ square units. $\newline$ What scale factor did Jennie use to go from Polygon $C$ to Polygon $D$ ?

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Scale drawings: word problems

Full solution

Q. Polygon

C

has an area of

7

square units. Jennie drew a scaled version of Polygon

C

and labeled it Polygon

D

. Polygon

D

has an area of

28

square units.

\newline

What scale factor did Jennie use to go from Polygon

C

to Polygon

D

?

Understand Relationship and Scale Factor: Understand the relationship between the areas of similar polygons and the scale factor. The area of similar polygons is proportional to the square of the scale factor. If Polygon C is scaled by a factor of $s$ to get Polygon D, then the area of Polygon D is $s^2$ times the area of Polygon C.
Set Up Equation for Scale Factor: Set up the equation to find the scale factor $s$ . $\text{Area of Polygon C} = 7$ square units. $\text{Area of Polygon D} = 28$ square units.The equation relating the areas through the scale factor is: $\text{Area of Polygon D} = (\text{scale factor})^2 \times \text{Area of Polygon C}$ . $28 = s^2 \times 7$ .
Solve for Scale Factor: Solve for the scale factor $s$ . Divide both sides of the equation by the area of Polygon C to isolate $s^2$ . $\frac{28}{7} = s^2$ . $4 = s^2$ .
Take Square Root to Find 's': Take the square root of both sides to solve for 's'. $\newline$ $\sqrt{4} = \sqrt{s^2}$ . $\newline$ $s = 2$ .

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