Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 5 Geometry
Problem

1) Samantha is playing with 100 wooden cubes. She first makes the biggest cube possible out of the 100 cubes. After she makes this cube, there are some small cubes left over. What is the width of the largest size cube she can make with the remaining cubes?

2) A quadrilateral has 4 lines of symmetry. Three of its vertices are (1,3), (7, 1) and (9, 7). What is the fourth vertex?

Problem

3) The area of a rectangle is 48 square feet. The lengths of the sides are whole numbers of feet. What is the largest perimeter the rectangle can have?

4) Ace, Berrit, and Calynn have a loop of string that measures 12 feet around. They each hold it with one hand and pull it taut to make a scalene triangle (none of the sides have the same length). After experimenting with different triangles they realize there is a range of values for the longest side. What are the low and high numbers for the range? Express your answer using inequalities with L representing the length of the longest side.

5) The length of the shortest trip from A to B, along the edges of the cube, is 3 edge lengths. How many different 3-edge trips are there from A to B?