Math  /  Geometry

QuestionState the side length of a square with an area of 363 cm2363 \mathrm{~cm}^{2} in simplified radical form. 15732 cm\frac{1573}{\sqrt{2}} \mathrm{~cm} 15732 cm\frac{1573}{2} \mathrm{~cm} 113 cm11 \sqrt{3} \mathrm{~cm} 786.5 cm\sqrt{786.5} \mathrm{~cm}

Studdy Solution

STEP 1

1. The shape in question is a square.
2. The area of the square is 363cm2 363 \, \text{cm}^2 .

STEP 2

1. Recall the formula for the area of a square.
2. Set up the equation to solve for the side length.
3. Simplify the expression to find the side length in radical form.
4. Compare the result with the given options.

STEP 3

Recall the formula for the area of a square:
Area=side length2 \text{Area} = \text{side length}^2

STEP 4

Set up the equation using the given area:
side length2=363 \text{side length}^2 = 363

STEP 5

Solve for the side length by taking the square root of both sides:
side length=363 \text{side length} = \sqrt{363}

STEP 6

Simplify 363\sqrt{363} to find the side length in simplified radical form:
First, factor 363 to find perfect squares: 363=3×121 363 = 3 \times 121 121=112 121 = 11^2
Thus: 363=3×112=113 \sqrt{363} = \sqrt{3 \times 11^2} = 11\sqrt{3}
The side length of the square is:
113cm \boxed{11\sqrt{3} \, \text{cm}}

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