Geometry Problems

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

1. A rectangular dog park has a perimeter of 60 yards. If its length is four times its width, what are its dimensions?
2. The length of a rectangle is 3 cm more than twice its width. If the perimeter of the rectangle is 72 cm, find its length and width.
3. Edvard Munch’s famous painting The Scream is a rectangle with perimeter 130 in. Its height is 22 in less than twice its width. What are its dimensions?
4. A farmer wants to build a rectangular pen using fencing, with a partition in the middle to separate the pigs and the sheep, as shown in the figure. She has a total of 144 feet of fencing to build the pen. If the width is two thirds the length, find the dimensions of the pen. Note: The partition is in the middle of the pen, parallel to the side of the pen that is called the length.
In triangle ABC, the measure of angle B is twice the measure of angle A. The measure of angle C is three times the measure of angle A. Find the measures of all three angles.
In triangle ABC, the measure of angle B is twice the measure of angle A. The measure of angle C is three times the measure of angle B. Find the measures of all three angles.
Find the measure of one base angle of an isosceles triangle if its vertex angle is 110 degrees.
Find the measure of the vertex angle of an isosceles triangle if each of its base angles if 48 degrees.