Danielle completely covered a square window using $$ 18.4 \mathrm{ft}^{2} $$ of contact paper without any overlap. Which measurement is closest to the side length of this window in feet? A 5 ft B 4 ft C 3 ft D 9 ft

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To find the side length of the square window, we can use the formula for the area of a square:

$$ \text{Area} = \text{side length}^2 $$

Given that the area of the window is $$18.4 \, \text{ft}^2$$, we can set up the equation:

$$ 18.4 = \text{side length}^2 $$

Now, we need to find the square root of 18.4 to determine the side length of the window. Let's calculate it.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{18.4}$$
- step1: Rewrite the expression:
  $$\sqrt{\frac{92}{5}}$$
- step2: Use the properties of radicals:
  $$\frac{\sqrt{92}}{\sqrt{5}}$$
- step3: Simplify the expression:
  $$\frac{2\sqrt{23}}{\sqrt{5}}$$
- step4: Multiply by the Conjugate:
  $$\frac{2\sqrt{23}\times \sqrt{5}}{\sqrt{5}\times \sqrt{5}}$$
- step5: Multiply the numbers:
  $$\frac{2\sqrt{115}}{\sqrt{5}\times \sqrt{5}}$$
- step6: Multiply the numbers:
  $$\frac{2\sqrt{115}}{5}$$
The side length of the window is approximately 4.29 ft.

Therefore, the closest measurement to the side length of the window in feet is 4 ft.
The side length of the window is approximately 4 feet.

Danielle completely covered a square window using \( 18.4 \mathrm{ft}^{2} \) of contact paper without any overlap. Which measurement is closest to the side length of this window in feet? A 5 ft B 4 ft C 3 ft D 9 ft

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