Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 8 Geometry
Problem
1) Jazmin is playing around with possible side lengths for isosceles triangles. She constructs one that has one side twice the length of another side. The lengths are whole numbers. What is the ratio of the area of the smallest possible isosceles triangle that fits this description to the area of the second smallest isosceles triangle that fits this description?
2) Rhonda wants to build a pendulum clock with the pendulum enclosed in a box with a glass door. Her pendulum will swing through 30 degrees and be 3 feet long. She's decided to use the length of the arc the pendulum swings through as the width for the box. What will the width be to the nearest tenth of a foot? (The arc is a section of the circumference determined by the angle.)
= 3.14

Problem
3) Tori measures the edges of a toy pyramid with square base and finds they are all 6 inches long. She wants to find the area of one of the triangular faces. What is the height, h, of one of the triangles? Give an exact answer or round to the nearest tenth of an inch. Figure is not to scale.
4) Reflect triangle ABC over the line l and then reflect the result over the y-axis. Where do A, B, and C go under the two reflections? Give the coordinates for each one.
5) In the picture is a representation of stretchable grabbing tongs. Segments AD, CF and EH are parallel to each other. Segments BC, DE and FG are parallel to each other. Angle AMB is 30 degrees. What is angle NFP?