Question

denise takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. if the piece of paper is 8 inches long and 3 inches wide, how long is the diagonal cut that denise made? if necessary, round to the nearest tenth. inches

Explanation:

Step1: Identify the formula

The paper is a rectangle, and the diagonal forms a right triangle with the length and width. We use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 8 \), \( b = 3 \), and \( c \) is the diagonal.

Step2: Substitute values

Substitute \( a = 8 \) and \( b = 3 \) into the formula: \( c = \sqrt{8^2 + 3^2} \)

Step3: Calculate squares

Calculate \( 8^2 = 64 \) and \( 3^2 = 9 \), so \( c = \sqrt{64 + 9} \)

Step4: Sum the values

Sum \( 64 + 9 = 73 \), so \( c = \sqrt{73} \)

Step5: Approximate the square root

\( \sqrt{73} \approx 8.5 \) (rounded to the nearest tenth)

Answer:

8.5