Question

1. (2x - 5)(2x - 5)
2. slide down the rope over a missing lawn daily or to your teammate on the other side of the river, how long rope do you need to accomplish this amazing feat (5 marks).
3. take the elevator down to the bottom floor, walk along the shore of the river for 150 m below the bridge and walk to your teammate. what is the total distance you need to travel (5 marks).

(there is a hand - drawn diagram below with labels: 10m, 200m, 20m, 150m and two stick figures)

Explanation:

Step1: Solve problem 1 (rope length)

The rope forms the hypotenuse of a right triangle with height $10\ \text{m}$ and horizontal distance $20\ \text{m}$. Use Pythagorean theorem:
$$c = \sqrt{a^2 + b^2}$$
$$c = \sqrt{10^2 + 20^2} = \sqrt{100 + 400} = \sqrt{500} = 10\sqrt{5} \approx 22.36\ \text{m}$$

Step2: Solve problem 2 (total distance)

Sum the given segment lengths:
$$150 + 200 + 20 = 370\ \text{m}$$

Answer:

1. Length of rope needed: $10\sqrt{5}\ \text{m}$ (or approximately $22.4\ \text{m}$)
2. Total travel distance: $370\ \text{m}$