Exercises

1. Leila is building a wooden wheelchair ramp for her grandma's house. The ramp must rise \(1.5\) m over a horizontal distance of \(6\) m. How long will the wooden surface of the ramp be?

2. Mackenzie wants to buy a round table for her new apartment. She measures the door to her apartment to be \(2\) m high and \(75\) cm wide. What is the diameter of the largest round table that Mackenzie can buy so that it will fit through her doorway?

3. Sarah leaves her home and drives south \(150\) km. Then she drives west \(70\) km. At this point, she drives north \(30\) km. Finally, she drives east \(20\) km. Draw a diagram of Sarah's trip. At the end of the trip, what is the straight line distance from Sarah's car to her home?

4. Determine the value of \(x\) in the diagram.

   

5. A triangle has side lengths \(4\), \(5\), and \(6\). 

   1. Do these side lengths form an acute triangle or an obtuse triangle?

   2. Determine which one of the lengths to change (and what to change it to) in order to create a right triangle with integer side lengths.

6. A warehouse is installing a pulley system from the corner of the floor, \(X\), to the opposite corner on the ceiling, \(Y\). This will require a rope that runs directly from \(X\) to \(Y\) and directly back to \(X\) in a straight line.

   The warehouse is \(100\) m by \(50\) m by \(20\) m. 

   How much rope is needed for the pulley system? 

   

7. The area of a right isosceles triangle is \(100\) cm². What is its perimeter? 

8. Triangle \(ABC\) has vertices \(A\left(-1,5\right)\), \(B\left(3,2\right)\), and \(C\left(-3,-3\right)\). Graph the triangle then determine its perimeter.

9. An electronics company is marketing their new "Super-Duper Widescreen" technology, which has an aspect ratio of \(12:5\).

   1. What would be the dimensions of a \(65\)-inch "Super-Duper Widescreen" monitor?

   2. Do you think that it is a good idea to use only the diagonal length to represent the size of a screen? Justify your response.