Question

1. the sail on a boat is shaped like an isosceles right - triangle. the side of the sail is 6√2 feet long. what is the length of each side? a. 3 feet b. 3√2 feet c. 2√6 feet d. 6 feet 3. the sides of a square are each 18 inches long. what is the diagonal? a. 18√2 inches b. 27 inches c. 18√3 inches d. 36 inches

Explanation:

1. For question 2:

• Recall the Pythagorean theorem for an isosceles - right triangle. In an isosceles right - triangle, if the length of each of the two equal sides is \(a\) and the hypotenuse is \(c\), then \(c^{2}=a^{2}+a^{2}=2a^{2}\), or \(c = a\sqrt{2}\). Given that the hypotenuse (the side of the sail) \(c = 6\sqrt{2}\) feet. Let the length of each of the equal sides be \(a\).
• From \(c = a\sqrt{2}\), we can solve for \(a\) by substituting \(c = 6\sqrt{2}\) into the equation:
• \(6\sqrt{2}=a\sqrt{2}\).
• Divide both sides of the equation by \(\sqrt{2}\), we get \(a = 6\) feet.

1. For question 3:

• Recall the Pythagorean theorem for a square. In a square of side length \(s\), if the diagonal is \(d\), then by the Pythagorean theorem \(d^{2}=s^{2}+s^{2}=2s^{2}\) (since in a square, the two sides forming a right - angle are of equal length \(s\)). Given \(s = 18\) inches.
• First, find \(d^{2}\): \(d^{2}=2s^{2}\), substituting \(s = 18\) inches, we have \(d^{2}=2\times(18)^{2}\).
• Then, find \(d\): \(d=\sqrt{2\times(18)^{2}}=\sqrt{2}\times18 = 18\sqrt{2}\) inches.

Step1: Solve for side of isosceles right - triangle

Use \(c = a\sqrt{2}\), substitute \(c = 6\sqrt{2}\), get \(a = 6\).

Step2: Solve for diagonal of square

Use \(d^{2}=2s^{2}\), substitute \(s = 18\), then \(d = 18\sqrt{2}\).

Answer:

1. D. 6 feet
2. A. \(18\sqrt{2}\) inches