Right Triangles
2D Shapes
Word Problems
Distance
3D Shapes
100
Find the missing side. Explain or show how you know.
5
(Pythagorean Triple)
100
A rectangle's dimensions are 2.7 feet by 6.5 feet. Find the measurement of the diagonal. Draw a picture with labels and show your work. Round your answer to the nearest hundredth and include units.
7.04 feet
100
Two joggers run 8 miles north and then 5 miles west. What is the shortest
distance, to the nearest tenth of a mile, they must travel to return to their
starting point? Draw a picture, show all your work, and include units.
9.4 miles
100
Find the distance between the given points. Show all your work. Round your answer to the nearest tenth.
d approx 8.6
100
Find the length of the diagonal. Show your work and include units.
13 yd
200
Find the missing side. Show all your work. Round your answer to the nearest hundredth.
c approx 7.28
200
A square's area is 121 square inches. Find the length of the diagonal. Show all work. Round your answer to the nearest integer and include units.
16 in
200
Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point? Draw a picture with labels, show your work, and include units.
4 feet
200
The mall is 5 miles west of your home. Your school is 5 miles south of the mall. What is the shortest distance from your home to school? Show all your work, round your answer to the nearest hundredth, and include units.
7.07 miles
200
Find the length indicated by x. You can assume the top of the pyramid is directly centered above the base. Show all work, round your answer to the nearest tenth, and include units.
21.9 ft
300
Find the missing side. Show all your work. Round your answer to the nearest tenth.
a approx 7.5
or
b approx 7.5
300
Find the height of this isosceles triangle. Show all your work. Leave your answer in radical form and include units.
sqrt55 cm
300
A suitcase measures 24 inches long and the diagonal is 30 inches long. How much material is needed to cover one face of the suitcase? Draw a picture with labels, show your work, and include units.
width: 18 in
face of suitcase (area): 432 square inches
300
Find the distance between the points (0, -2) and (-5, -1). Show all your work. Leave your answer in radical form.
d = sqrt26
300
A wooden plank of the greatest possible length is placed inside a garden shed. Use the diagram to calculate the length of the plank of wood to one decimal place. Show all your work and include units.
3.1 m
400
Does this picture show a right triangle? If yes, which side is the hypotenuse?
Show all your work to justify your answer.
Not a right triangle.
6^2+8^2=9^2
36+64 = 81
100 ne 81
400
Given the diagram below, find the length of the rectangle's diagonal. Show all your work. Round your answer to the nearest tenth and include units.
8.2 m
400
You're locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. The ladders at the store are only sold by whole number lengths. What length of ladder do you need to reach the window? Draw a picture, show your work, and include units.
27 feet long
400
What was the height of the tree before it fell? Show all your work, round your answer to the nearest integer, and include units.
fallen part: 13 m
original tree height: 16 m
400
Find the length indicated by x (top back left corner to bottom front right corner). Show all work, round your answer to the nearest tenth, and include units.
x approx 23.4 cm
500
Is a triangle with the sides 7.2, 7.5, and 2.1 a right triangle? If yes, which side is the hypotenuse? You must show all your work to justify your answer.
It is a right triangle. 7.5 is the hypotenuse (longest side).
7.2^2+2.1^2=7.5^2
51.84 + 4.41=56.25
56.25=56.25
500
Given the diagram of the isosceles triangle below, find the perimeter of the triangle. Show all your work. Round your answer to the nearest tenth and include units.
Base of triangle: 14.3 cm
Perimeter: 34.3 cm
500
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? Draw a picture with labels, show your work, and include units.
Distance through pond: 53 m
Meters saved: 22 m
500
[Double Points]: Name a point that is 2 away from (−1, 5). Justify or show how you found your answer.
(0, 6), (0, 4), (-2, 6), or (-2, 4)
500
A package is in the shape of a cube. The height of the package is 10 inches. What is the diagonal length of the package? Draw a picture, show your work, round to the nearest hundredth, and include units.
17.32 in