Problem 1: Hypotenuse of a 6-8 triangle
Find the length of the hypotenuse.
Problem 2: Hypotenuse of a 5-12 triangle
A right triangle has legs of 5 ft and 12 ft. Find the hypotenuse.
Problem 3: Find the missing leg
Find the missing leg.
Problem 4: Missing leg of a 7-25 triangle
The hypotenuse of a right triangle is 25 in. One leg is 7 in. Find the other leg.
Problem 5: Legs 9 and 12
Find the hypotenuse of a right triangle with legs 9 in and 12 in.
Problem 6: Hypotenuse that is not whole
A right triangle has legs of 4 ft and 7 ft. Find the hypotenuse. Give the exact value and then round to the nearest tenth.
Problem 7: Leg that is not whole
The hypotenuse of a right triangle is 13 in. One leg is 9 in. Find the other leg to the nearest tenth.
Problem 8: Squares on the sides
The squares built on the legs of a right triangle have areas 36 square units and 64 square units. Find the area of the square on the hypotenuse and the length of the hypotenuse.
Problem 9: Area proof with numbers
A square with side length 17 in. holds four congruent right triangles with legs 5 in. and 12 in. and a tilted square. (a) Find the area of the large square. (b) Find the total area of the four triangles. (c) Find the area of the tilted square. (d) Find its side length.
Problem 10: Explain the proof
In the square-and-triangles figure, the large square has side \(a+b\) and the tilted square has side \(c\). Explain, using areas, why \(a^{2}+b^{2}=c^{2}\).
Problem 11: Converse: 9, 12, 15
A triangle has sides 9 in., 12 in. and 15 in. Is it a right triangle? Explain.
Problem 12: Converse: 7, 10, 12
A triangle has sides 7 ft, 10 ft and 12 ft. Is it a right triangle? Explain.
Problem 13: Which sets are right triangles?
Which of these side lengths form a right triangle? Show the check for each.
- 8, 15, 17
- 6, 7, 10
- 20, 21, 29
- 11, 12, 18
Problem 14: Perimeter and area
The legs of a right triangle measure 10 in. and 24 in. Find the perimeter and the area.
Problem 15: Diagonal of a square
A square picture frame is 9 in. on each side. Find the length of its diagonal to the nearest tenth.
Problem 16: Height of an isosceles triangle
An isosceles triangle has a base of 12 in. and two equal sides of 10 in. Find its height. Then find its area.
Problem 17: Diagonal of a prism
A rectangular prism is 8 in. long, 6 in. wide and 24 in. tall. Find the length of the space diagonal, from a bottom corner to the opposite top corner.
Problem 18: Ladder against a house
A 25-ft ladder leans against a house. Its base is 7 ft from the wall. How high up the wall does the ladder reach?
Problem 19: TV screen diagonal
A TV screen is 24 in. wide and 18 in. tall. TVs are sold by the length of the screen diagonal. What size is this TV?
Problem 20: Little League throw
A Little League infield is a square with 60 ft between bases. The catcher at home plate throws to second base. How far is the throw to the nearest tenth of a foot?
Problem 21: Is the corner square?
Sofia builds a rectangular door frame. She measures 60 in. along the bottom and 80 in. up the side. The diagonal between those two points measures 100 in. Is the corner a right angle? Explain.
Problem 22: Walk east and north
Jamal walks 0.9 mi east and then 1.2 mi north. How far is he from where he started, in a straight line?
Problem 23: Longest rod in a box
A storage box is 12 in. long, 9 in. wide and 8 in. tall. Maya wants to store a straight rod that is 17 in. long. Will it fit inside the box? Explain.
See every chapter on the Grade 8 math page.