Final answer:
To construct rectangle PQRS with PQ = 10.4 and ∠QPR = 32°, use a ruler to draw PQ, a protractor to form the angle, and a ruler to measure sides PS and PR. PS equals PQ, thus PS = 10.4. Use the Pythagorean theorem to calculate PR and then measure it with the ruler.
Step-by-step explanation:
To construct a rectangle PQRS with PQ equal to 10.4 and an angle ∠QPR of 32°, start by drawing line PQ to the specified length using a ruler. Then, use a protractor to create a 32° angle at point P to determine the direction of line PR. Extend PR until it intersects with the line that is perpendicular to PQ and completes the rectangle. Measure the length of PS and PR with a ruler. By the properties of rectangles, PQ = PS, so PS is also 10.4 units. To find PR's length, you can use the Pythagorean theorem since triangle PQR is a right triangle (with a 90° angle at Q).
To find PR, we can apply the Pythagorean theorem (c² = a² + b²), considering PR as the hypotenuse c, and PQ & QR as the other two sides a and b respectively. Since we have PQ and we know that QR = PS (as this is a rectangle and opposite sides are equal), we will substitute 10.4 for both a and b in the Pythagorean theorem equation.
c² = 10.4² + 10.4² leads to c² = 2(10.4²), and solving for c will give us the length of PR. Finally, you measure the length of PR with the ruler to confirm the calculation.