Question

1. a photograph has been enlarged by a scale factor of 1.75. if the enlarged photo has an area of 675 cm², what is the area of the original photo?

Explanation:

Step1: Recall area - scale factor relationship

The ratio of the areas of two similar figures is equal to the square of the scale factor. Let the scale factor be $k = 1.75$, the area of the enlarged photo be $A_{2}=675\ cm^{2}$, and the area of the original photo be $A_{1}$. Then $\frac{A_{2}}{A_{1}}=k^{2}$.

Step2: Solve for the original - area

We can re - arrange the formula $\frac{A_{2}}{A_{1}}=k^{2}$ to get $A_{1}=\frac{A_{2}}{k^{2}}$. Substitute $A_{2} = 675$ and $k = 1.75$ into the formula. So $A_{1}=\frac{675}{1.75^{2}}=\frac{675}{3.0625}=\frac{675\times10000}{30625}=\frac{6750000}{30625}=220.4545\ cm^{2}\approx220.45\ cm^{2}$

Answer:

$220.45\ cm^{2}$