Practice Proportional Geometry in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Using ratios and proportions to relate corresponding measurements in similar or scaled geometric figures.
Similar triangles have proportional sides: if one side doubles, all sides double.
Example 1
easyTwo similar triangles have corresponding sides in the ratio 3:5. If the shorter triangle has a base of 9 cm, what is the base of the larger triangle?
Example 2
mediumA 6 ft tall person casts a shadow 4 ft long. At the same time, a tree casts a shadow 14 ft long. How tall is the tree?
Example 3
mediumTwo similar rectangles have widths 4 cm and 10 cm. If the smaller rectangle has length 6 cm, find the length of the larger rectangle.
Example 4
easyTwo similar rectangles have widths 5 cm and 15 cm. What is the scale factor from the smaller to the larger?
Example 5
hardOn a map, 1 cm represents 50 km. Two cities are 3.6 cm apart on the map. What is the actual distance? Also, a lake has an area of 4 cm² on the map. What is its actual area in km²?