Question

question 9
10 pts
g.gsr.6.1 (hc)
a square floor tile has a diagonal that is 10 inches long. how long are the side lengths?
10√2 inches
5√2 inches
5 inches
10 inches

Explanation:

Step1: Recall square diagonal formula

For a square with side length \( s \), the diagonal \( d \) is related by \( d = s\sqrt{2} \) (from Pythagorean theorem, as square's diagonal forms a right triangle with two sides).

Step2: Solve for side length \( s \)

Given \( d = 10 \) inches, substitute into formula: \( 10 = s\sqrt{2} \). Solve for \( s \): \( s=\frac{10}{\sqrt{2}} \). Rationalize denominator: \( s = \frac{10\sqrt{2}}{2}=5\sqrt{2} \) inches.

Answer:

B. \( 5\sqrt{2} \) inches