A city planning commission recently voted to restrict the size of home remodels by limiting the floor area to lot area ratio to a maximum of 0.35 to 1 . Under these guidelines, (a) What would be the maximum allowable size of a remodel on an \( 11,800 \mathrm{sq} \mathrm{ft} \) lot? (b) What size lot would be required in order to create a 2905 sq ft remodel? (a) The maximum allowable size of a remodel on an \( 11,800 \mathrm{sq} \mathrm{ft} \) lot would be \( \square \mathrm{sq} \mathrm{ft} \)

To determine the maximum allowable size of a remodel on an \( 11,800 \mathrm{sq} \mathrm{ft} \) lot under a floor area to lot area ratio of \( 0.35 \), you multiply the lot size by that ratio: \[ \text{Maximum size} = 11,800 \mathrm{sq} \mathrm{ft} \times 0.35 = 4,130 \mathrm{sq} \mathrm{ft} \] So, the maximum allowable size of a remodel on an \( 11,800 \mathrm{sq} \mathrm{ft} \) lot would be \( 4,130 \mathrm{sq} \mathrm{ft} \). To find the size of the lot required to create a \( 2,905 \mathrm{sq} \mathrm{ft} \) remodel, you'd use the formula of dividing the desired remodel size by the ratio: \[ \text{Required lot size} = \frac{2,905 \mathrm{sq} \mathrm{ft}}{0.35} \approx 8,300 \mathrm{sq} \mathrm{ft} \] Therefore, a lot of approximately \( 8,300 \mathrm{sq} \mathrm{ft} \) would be required for a \( 2,905 \mathrm{sq} \mathrm{ft} \) remodel. This kind of zoning guideline isn’t just random; it's a common practice to maintain the character and scale of neighborhoods. Such regulations help ensure that larger homes don't overshadow smaller ones, keeping communities harmonious and attractive. Ever wondered how these zoning laws can create a juxtaposition of old and new? Sometimes they can actually inspire creativity in home design! Homeowners might explore unique architectural solutions or adaptive reuse of spaces, blending modern updates with historical charm. So, the constraints can often spark innovative remodeling ideas!