Question 10(Multiple Choice Worth 1 points)

(04.03 MC)

Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Side AB measures 3.16 units. Diagonal BD measures 7.07 units. Round your answer to the nearest hundredth.



 12.64 18.96 25.28 26.78

To find the total length of the tiles needed to surround the pool ABCD, we need to calculate the perimeter of quadrilateral ABCD. Given:
- \(AB = 3.16\) units
- \(BD = 7.07\) units

We need to calculate the lengths of \(BC\) and \(CD\). We will use the coordinates provided:
- \(A(0, 4)\)
- \(B(3, 5)\)
- \(C(5, -1)\)
- \(D(2, -2)\)

### Calculations
1. **Length of \(BC\):**
\[ BC = \sqrt{(5 - 3)^2 + (-1 - 5)^2} = \sqrt{2^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32 \]

2. **Length of \(CD\):**
\[ CD = \sqrt{(5 - 2)^2 + (-1 - (-2))^2} = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.16 \]

3. **Length of \(DA\):**
\[ DA = \sqrt{(2 - 0)^2 + (-2 - 4)^2} = \sqrt{2^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32 \]

### Perimeter Calculation
Summing up all the sides:
\[ \text{Perimeter} = AB + BC + CD + DA \]
\[ \text{Perimeter} = 3.16 + 6.32 + 3.16 + 6.32 = 18.96 \]

### Answer
The total length of the tiles needed to surround the pool is:
\[ 18.96 \]

**Answer: 18.96**

Learn how to calculate the perimeter of a pool ABCD surrounded by tiles. This problem involves using the distance formula and perimeter formula for quadrilaterals. Suitable for students in Grades 9-10.

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