This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the steps to construct the square WXYZ and the measurement of its side. Step 1: Draw the diagonal Draw a line segment WY of length 8 cm. This will be one of the diagonals of the square. Step 2: Construct the perpendicular bisector Construct the perpendicular bisector of WY. • With W as the center and a radius greater than 4 cm (half of 8 cm), draw arcs above and below WY. • With Y as the center and the same radius, draw arcs that intersect the previously drawn arcs. • Draw a straight line connecting the two intersection points. This line is the perpendicular bisector of WY. Let the point where it intersects WY be O. Step 3: Locate the other vertices The diagonals of a square bisect each other at 90^. So, O is the center of the square, and the other diagonal XZ will lie along the perpendicular bisector. • With O as the center and a radius of 4 cm (half of the diagonal length), draw arcs on the perpendicular bisector. Mark the points where these arcs intersect the bisector as X and Z. Step 4: Complete the square Connect the points W, X, Y, and Z in order to form the square WXYZ. Step 5: Measure the length of one side In a square, if s is the side length and d is the diagonal length, they are related by the Pythagorean theorem: s^2 + s^2 = d^2. 2s^2 = d^2 s^2 = (d^2)/(2) s = sqrt((d^2)/(2)) = (d)/(sqrt(2)) Given the diagonal d = 8 cm: s = 8 cmsqrt(2) To rationalize the denominator: s = 8sqrt(2)2 cm s = 4sqrt(2) cm Calculating the numerical value: s ≈ 4 × 1.4142 cm s ≈ 5.6568 cm The length of one side of the square is approximately 5.66 cm. That's 2 down. 3 left today — send the next one.