Finding a missing side with the Pythagorean theorem. Game on.

Finding a missing side with the Pythagorean theorem is a grade 8 math skill aligned to Common Core standard 8.G.B.7: apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 finding a missing side with the pythagorean theorem problems our math games drill.

CCSS 8.G.B.710 questions in the bank
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Warm-upeasy

The legs of a right triangle are 1212 inches and 3535 inches long. How long is the hypotenuse?

The legs are 1212 and 3535. By the Pythagorean theorem, 122+352=144+1,225=1,36912^{2} + 35^{2} = 144 + 1{,}225 = 1{,}369, so the hypotenuse is 1,369=37\sqrt{1{,}369} = 37.

Mid-gameeasy

A right triangle has leg lengths 1616 ft and 3030 ft. Find the length of the hypotenuse.

The legs are 1616 and 3030. By the Pythagorean theorem, 162+302=256+900=1,15616^{2} + 30^{2} = 256 + 900 = 1{,}156, so the hypotenuse is 1,156=34\sqrt{1{,}156} = 34.

Mid-gameeasy

If a right triangle has a hypotenuse of 3030 yards and one leg of 1818 yards, what is the other leg?

Let the missing leg be xx. Then x2+182=302x^{2} + 18^{2} = 30^{2}, so x2=302−182=900−324=576x^{2} = 30^{2} - 18^{2} = 900 - 324 = 576 and x=576=24x = \sqrt{576} = 24.

Mid-gameeasy

Find the hypotenuse of a right triangle whose legs are 2121 m and 2828 m.

The legs are 2121 and 2828. By the Pythagorean theorem, 212+282=441+784=1,22521^{2} + 28^{2} = 441 + 784 = 1{,}225, so the hypotenuse is 1,225=35\sqrt{1{,}225} = 35.

Mid-gameeasy

The hypotenuse of a right triangle measures 2626 meters, and one leg measures 2424 meters. What is the length of the second leg?

Let the missing leg be xx. Then x2+242=262x^{2} + 24^{2} = 26^{2}, so x2=262−242=676−576=100x^{2} = 26^{2} - 24^{2} = 676 - 576 = 100 and x=100=10x = \sqrt{100} = 10.

Mid-gamemedium

The shorter leg of a right triangle is 1111 centimeters and the longer leg is 6060 centimeters. What is the length of the hypotenuse?

The legs are 1111 and 6060. By the Pythagorean theorem, 112+602=121+3,600=3,72111^{2} + 60^{2} = 121 + 3{,}600 = 3{,}721, so the hypotenuse is 3,721=61\sqrt{3{,}721} = 61.

Mid-gamemedium

A right triangle has hypotenuse 3939 inches. One of its legs measures 1515 inches. What is the measure of the remaining leg?

Let the missing leg be xx. Then x2+152=392x^{2} + 15^{2} = 39^{2}, so x2=392−152=1,521−225=1,296x^{2} = 39^{2} - 15^{2} = 1{,}521 - 225 = 1{,}296 and x=1,296=36x = \sqrt{1{,}296} = 36.

Buzzer beatermedium

In a right triangle, one leg is 99 feet and the hypotenuse is 4141 feet. How long is the other leg?

Let the missing leg be xx. Then x2+92=412x^{2} + 9^{2} = 41^{2}, so x2=412−92=1,681−81=1,600x^{2} = 41^{2} - 9^{2} = 1{,}681 - 81 = 1{,}600 and x=1,600=40x = \sqrt{1{,}600} = 40.

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Tests that cover finding a missing side with the pythagorean theorem:
NAEPSBACPSAT 8/9SC READYNC EOG/EOC
More Grade 8 skills
Interpreting linear parametersScatterplots and trend linesLinear coefficient interpretationsPolygon angle formulasPythagorean theoremTwo-way tablesGraphing linear equationsLinear functions with an unknown constantAll Grade 8 practice →

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