2. Elena finds that the area of a house on a scale drawing is 25 square inches. Theactual area of the house is 2,025 square feet. What is the scale of the drawing?
Accepted Solution
A:
Answer:The scale of the drawing is [tex]\frac{1}{9}\ \frac{in}{ft}[/tex]Step-by-step explanation:we know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetz ----> the scale factorx ----> the area of an house on a scale drawing in square inchesy ---> the actual area of the house in square feet[tex]z^2=\frac{x}{y}[/tex]we have[tex]x=25\ in^2[/tex][tex]y=2,025\ ft^2[/tex]substitute[tex]z^2=\frac{25}{2,025}[/tex]simplify[tex]z^2=\frac{1}{81}[/tex]square root both sides[tex]z=\frac{1}{9}\ \frac{in}{ft}[/tex]thereforeThe scale of the drawing is [tex]\frac{1}{9}\ \frac{in}{ft}[/tex]