Planting Equal Plots

Strategies and Hints

  1. The Pythagorean Theorem can be used to find the angle. Since 122 + 92 = 152, the angle must be 9Oo.

  2. The total area of the garden is 114 square feet, so each of the 19 plots is 6 square feet.

  3. The ratio of the area of the triangle to the area of the rectangle is 9:10. This suggests that the triangle will contain 9 of the plots; the rectangle, 10.

  4. The triangle can be divided into 4 congruent right triangles. This suggests that the shape of each of the 19 plots will be a triangle.

Solution

Note: the rectangular area could also consist of 10 rectangular plots, 4 ft by 1.5 ft. 2 ft by 3 ft. and so on.