Name: ____________________________________
Date: __________
Core: ______
Pythagorean Theorem Application
Use the converse to determine whether a triangle with the given side lengths is a right triangle. Show your
work. If it is a right triangle, draw an appropriate diagram; label the sides and right angle.
1.) 9, 12, 15
2.) 25, 16, 9
3.) 8, 8, 11
Solve each of the following problems. Draw a picture. Show all work. Round your answers to the nearest
tenth, if necessary.
4.) A wheelchair ramp is constructed to rise 1 foot off the ground and extends 12 feet along the ground. How
long will the wheelchair ramp be?
5.) Mark needs to wash the windows on the second floor of a building. He knows the windows are 12 feet
above the ground. Because of dense shrubbery, he has to put the base of the ladder 5 feet from the building.
What ladder length does he need?
6.) Brianna walks in the park everyday using the trail shown. The two legs are 24 feet and 36 feet. If she walks
3 full laps, how far does she walk daily?
7.) Alex attaches a diagonal brace to a rectangular-shaped picture frame. If the dimensions of the frame are
30 inches by 40 inches, what is the length of the brace?
8.) A television is identified by the diagonal measurement of the screen. A television has a 36-inch screen (the
diagonal) whose height is 22 inches. What is the length of the television screen?
9.) What is the diagonal length of a square that has a side length of 12 inches?
10.) A rescue boat leaves Walk Dock and travels 18 miles due north to haul in a sailing vessel stranded in the
middle of a lake. After attaching a cable, the rescue boat hauls the sailing vessel 80 miles due east to Blue
Haven Dock. Determine the direct distance from Walker Dock to Blue Haven Dock.
11.) Jorge is installing a gravel path along the diagonal of a rectangular garden. The garden measures 24 feet
by 32 feet long. Find the length of the diagonal.
If the path is 2 feet wide, and gravel costs $2.50 a square foot, how much will it cost to install the gravel path?
12.) The eighth-grade math class keeps a flower garden in the front of the building. The garden is in the shape
of a right triangle, and the two legs are 9 feet and 12 feet. The class wants to install a 3-foot-high picket fence
around the garden to keep students from stepping onto the flowers.
The picket fence they need costs $5 a linear foot. How much will the fence cost? Do not calculate sales tax.
Show your work and justify your solution.
Use the Pythagorean Theorem to find the distance between the two points.
13.) Find the distance between A and C.
14.) Find the distance between (1, 2) and (3, -2).
Assume that each block is one unit.
15.) Find the distance between point A and point B.
16.) Find the distance between the two points on the coordinate plane to the right.
17.) Find the distance between the two points on the
coordinate plane to the left.
18.) Find the distance between the two points on the coordinate plane to
the right.
19.) Find the distance between B and D. Assume that each block is 1 unit.
20.) Find the length of x.
21.) Find the length marked, x, in the diagram below.