(3) Terri makes a quilt using three sizes of
fabric squares. The side length of each
fabric square is the square root of the
area. The areas of the fabric squares are
29,40 , and 62 square inches. Which
could be the approximate side length of a
square of the quilt?
A. 2.9 in .
B. 5.4 in .
C. 6.7 in .
D. 8.1 in .

Question

UpStudy AI · Accepted Answer

To find the approximate side lengths of the fabric squares, we need to calculate the square root of each area provided. The areas of the fabric squares are 29, 40, and 62 square inches.

Let's calculate the side lengths step by step:

1. **Calculate the side length for the area of 29 square inches:**
   $$
   s_1 = \sqrt{29}
   $$

2. **Calculate the side length for the area of 40 square inches:**
   $$
   s_2 = \sqrt{40}
   $$

3. **Calculate the side length for the area of 62 square inches:**
   $$
   s_3 = \sqrt{62}
   $$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{62}$$
Calculate or simplify the expression $$ \sqrt(29) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{29}$$
Calculate or simplify the expression $$ \sqrt(40) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{40}$$
- step1: Write as a product:
  $$\sqrt{4\times 10}$$
- step2: Write in exponential form:
  $$\sqrt{2^{2}\times 10}$$
- step3: Use the properties of radicals:
  $$\sqrt{2^{2}}\times \sqrt{10}$$
- step4: Simplify the root:
  $$2\sqrt{10}$$
The approximate side lengths of the fabric squares are as follows:

1. For the area of 29 square inches:
   $$
   s_1 \approx 5.39 \text{ in}
   $$

2. For the area of 40 square inches:
   $$
   s_2 \approx 6.32 \text{ in}
   $$

3. For the area of 62 square inches:
   $$
   s_3 \approx 7.87 \text{ in}
   $$

Now, let's compare these results with the options provided:

A. 2.9 in  
B. 5.4 in  
C. 6.7 in  
D. 8.1 in

The closest approximate side lengths from our calculations are:
- $$5.39$$ in (which is close to option B: 5.4 in)
- $$6.32$$ in (which is close to option C: 6.7 in)
- $$7.87$$ in (which is close to option D: 8.1 in)

Among the options, the most appropriate approximate side length of a square of the quilt is:

**B. 5.4 in.**
The approximate side lengths are 5.4 in, 6.7 in, and 8.1 in. So, the closest option is B. 5.4 in.

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