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 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 lot would be

Ask by Marshall Barker. in the United States

Jan 11,2025

Question

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 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 lot would be

Ask by Marshall Barker. in the United States

Jan 11,2025

UpStudy AI · Accepted Answer

To solve the problem, we need to understand the floor area to lot area ratio, which is given as a maximum of 0.35 to 1. This means that for every 1 square foot of lot area, the maximum allowable floor area (remodel size) is 0.35 square feet.

### Part (a)
We need to find the maximum allowable size of a remodel on an $$ 11,800 \mathrm{sq} \mathrm{ft} $$ lot.

1. **Identify the known values:**
   - Lot area $$ L = 11,800 \mathrm{sq} \mathrm{ft} $$
   - Maximum ratio $$ R = 0.35 $$

2. **Calculate the maximum allowable size of the remodel $$ A $$:**
   $$
   A = R \times L
   $$

Now, substituting the known values into the equation:

$$
A = 0.35 \times 11,800
$$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$0.35\times 11800$$
- step1: Multiply the numbers:
  $$4130$$
The maximum allowable size of a remodel on an $$ 11,800 \mathrm{sq} \mathrm{ft} $$ lot would be $$ 4130 \mathrm{sq} \mathrm{ft} $$.

### Part (b)
Next, we need to determine what size lot would be required in order to create a $$ 2905 \mathrm{sq} \mathrm{ft} $$ remodel.

1. **Identify the known values:**
   - Desired remodel size $$ A = 2905 \mathrm{sq} \mathrm{ft} $$
   - Maximum ratio $$ R = 0.35 $$

2. **Calculate the required lot area $$ L $$:**
   $$
   L = \frac{A}{R}
   $$

Now, substituting the known values into the equation:

$$
L = \frac{2905}{0.35}
$$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2905}{0.35}$$
- step1: Convert the expressions:
  $$\frac{2905}{\frac{7}{20}}$$
- step2: Multiply by the reciprocal:
  $$2905\times \frac{20}{7}$$
- step3: Reduce the numbers:
  $$415\times 20$$
- step4: Multiply the numbers:
  $$8300$$
The size lot required in order to create a $$ 2905 \mathrm{sq} \mathrm{ft} $$ remodel would be $$ 8300 \mathrm{sq} \mathrm{ft} $$.

### Summary of Results:
- (a) The maximum allowable size of a remodel on an $$ 11,800 \mathrm{sq} \mathrm{ft} $$ lot is $$ 4130 \mathrm{sq} \mathrm{ft} $$.
- (b) The size lot required for a $$ 2905 \mathrm{sq} \mathrm{ft} $$ remodel is $$ 8300 \mathrm{sq} \mathrm{ft} $$.
(a) The maximum allowable size of a remodel on an $$ 11,800 \mathrm{sq} \mathrm{ft} $$ lot is $$ 4130 \mathrm{sq} \mathrm{ft} $$. (b) A lot of $$ 8300 \mathrm{sq} \mathrm{ft} $$ is required to create a $$ 2905 \mathrm{sq} \mathrm{ft} $$ remodel.

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