The Garcia family is going to remodel their basement. The basement floor has an area of 470 square feet On the blueprint, the basament has an
area of 75.2 square inches. The perimeter of the basement on the blueprint is 348 inches. What is the perimeter of the real basement?
for full credit, you must:

Show all your work.

Round your answer to the nearest tenth of a foot.

Question

The Garcia family is going to remodel their basement. The basement floor has an area of 470 square feet On the blueprint, the basament has an
area of 75.2 square inches. The perimeter of the basement on the blueprint is 348 inches. What is the perimeter of the real basement?
for full credit, you must:

Show all your work.
Round your answer to the nearest tenth of a foot.

UpStudy AI · Accepted Answer

To find the perimeter of the real basement, we first need to determine the scale factor between the blueprint and the real basement.

Given:
- Area of the basement floor = 470 square feet
- Area of the basement on the blueprint = 75.2 square inches
- Perimeter of the basement on the blueprint = 348 inches

First, let's convert the area of the basement floor from square feet to square inches:
$$ 470 \text{ square feet} = 470 \times 144 \text{ square inches} = 67680 \text{ square inches} $$

Now, we can find the scale factor by dividing the area of the basement floor by the area of the basement on the blueprint:
$$ \text{Scale factor} = \frac{67680 \text{ square inches}}{75.2 \text{ square inches}} $$

Next, we can use the scale factor to find the perimeter of the real basement by multiplying the perimeter of the basement on the blueprint by the scale factor:
$$ \text{Perimeter of the real basement} = \text{Scale factor} \times \text{Perimeter of the basement on the blueprint} $$

Let's calculate the scale factor and then the perimeter of the real basement.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{67680}{75.2}$$
- step1: Convert the expressions:
  $$\frac{67680}{\frac{376}{5}}$$
- step2: Multiply by the reciprocal:
  $$67680\times \frac{5}{376}$$
- step3: Reduce the numbers:
  $$180\times 5$$
- step4: Multiply the numbers:
  $$900$$
The scale factor is 900.

Now, we can find the perimeter of the real basement by multiplying the perimeter of the basement on the blueprint by the scale factor:
$$ \text{Perimeter of the real basement} = 900 \times 348 \text{ inches} $$

Let's calculate the perimeter of the real basement.
Calculate the value by following steps:
- step0: Calculate:
  $$900\times 348$$
- step1: Multiply the numbers:
  $$313200$$
The perimeter of the real basement is 313200 inches.

To convert this to feet, we divide by 12:
$$ \text{Perimeter of the real basement in feet} = \frac{313200}{12} $$

Let's calculate the perimeter of the real basement in feet.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{313200}{12}$$
- step1: Reduce the numbers:
  $$\frac{26100}{1}$$
- step2: Calculate:
  $$26100$$
The perimeter of the real basement is 26100 feet.

Rounding to the nearest tenth of a foot, the perimeter of the real basement is 26100 feet.
The perimeter of the real basement is 26,100 feet.

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