Question

the area of a square is 81 square centimeters. find the length of a side. s = 9 cm find the length of the diagonal. (round to nearest hundredth) diagonal = cm

Explanation:

Step1: Recall the formula for the diagonal of a square

For a square with side length \( s \), the diagonal \( d \) can be found using the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides of the square, so \( d = s\sqrt{2} \).

Step2: Substitute the side length into the formula

We know the side length \( s = 9 \) cm. So, \( d = 9\sqrt{2} \).

Step3: Calculate the numerical value

\( \sqrt{2} \approx 1.4142 \), so \( 9\sqrt{2} \approx 9\times1.4142 = 12.7278 \).

Step4: Round to the nearest hundredth

Rounding \( 12.7278 \) to the nearest hundredth gives \( 12.73 \).

Answer:

\( 12.73 \)