Exercises


  1. A tennis court is approximately \(24\) m in length and \(8\) m in width. A soccer field is approximately \(100\) m in length and \(75\) m in width. Are the length and the width in the same proportion for each of these fields?
  2. An original image has a length of \(12\) cm and width of \(8\) cm. The image is enlarged.
    1. If the enlarged image has length \(30\) cm and width \(15\) cm, then explain how you know the enlarged image is not in proportion with the original.
    2. If the enlarged image has a length of \(30\) cm and is in proportion with the original, then what is the width?
    3. If the enlarged image has a width of \(15\) cm and is in proportion with the original, then what is the length?
  3. Consider the following figures. In each figure, the polygon is divided into identical shapes.
    Figure A
    A triangle is divided into 4 equal parts, 1 of the parts is shaded.
    Figure B
    A hexagon is divided into 6 equal parts, 2 of the parts are shaded.
    Figure C
    A square is divided into 16 equal parts, 4 of the parts are shaded.
    Figure D
    A rectangle is divided into 9 equal parts, 3 of the parts are shaded.
    Which figures have the same proportion of shaded area to total area?
  4. You are offered \($25\) to make \(12\) beaded bracelets. The rate of payment is proportional to the number of bracelets that you make. 
    1. How much money would you be paid to make \(60\) bracelets?
    2. If you were paid \($175\), then how many bracelets did you make?
  5. While making the bracelets from question 4, you record the time it takes to make each batch of \(12\) bracelets.
    Number of Bracelets  Time Spent (min)
    \(12\) \(36\)
    \(24\) \(60\)
    \(36\) \(78\)
    \(48\) \(90\)
    1. Is the number of bracelets that you can make proportional to the time spent? Explain your reasoning.
    2. Why might each batch of \(12\) bracelets not take the same amount of time to complete? 
  6. The side lengths of \(\Delta ABC\) are \(3\), \(4\), and \(5\) units.
    1. \(\Delta ABC\) is enlarged, in proportion, and the largest side length of the enlarged triangle is \(15\) units. What are the lengths of the other two sides of this triangle?
    2. \(\Delta ABC\) is reduced, in proportion, and the smallest side length of the reduced triangle is \(0.75\). What are the lengths of the other two sides of this triangle?
  7. The length and width of two rectangles are proportional. This means that if the dimensions of the first rectangle are \(\ell\) and \(w\) and the dimensions of the second rectangle are \(L\) and \(W\) then the ratios \(\ell : w\) and \(L : W\) are equivalent.
    1. If the length of the first rectangle and the width of the second rectangle are both \(5\) mm (that is, \( \ell = 5\) and \(W = 5\)), then give two possibilities for the remaining dimensions of the rectangles.
    2. If the width of the first rectangle is \(2\) cm and the width of the second rectangle is \(4\) cm (that is, \(w =2\) and \(W=4\)), then what is the ratio of the areas of the rectangles?