Pythagorean theorem Practice Questions (Grade 8)

Pythagorean theorem practice

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 15 pythagorean theorem problems our math games drill.

CCSS 8.G.B.715 questions in the bank

Question 1easy

A right triangle has legs $3$ and $4$ . What is the hypotenuse?

$3^2 + 4^2 = 9 + 16 = 25$ , so the hypotenuse is $\sqrt{25} = 5$ .

Question 2easy

A right triangle has one leg $5$ and hypotenuse $13$ . What is the other leg?

$13^2 - 5^2 = 169 - 25 = 144$ , so the other leg is $\sqrt{144} = 12$ .

Question 3easy

What is the horizontal distance from $(1, 5)$ to $(7, 5)$ ?

Both points have $y = 5$ , so the distance is $|7 - 1| = 6$ .

Question 4easy

A right triangle has legs $5$ and $12$ . What is the hypotenuse?

$5^2 + 12^2 = 25 + 144 = 169$ , so the hypotenuse is $\sqrt{169} = 13$ .

Question 5easy

A right triangle has hypotenuse $17$ and one leg $8$ . How long is the other leg?

$17^2 - 8^2 = 289 - 64 = 225$ , so the other leg is $\sqrt{225} = 15$ .

Question 6easy

A right triangle has legs $8$ and $15$ . What is the hypotenuse?

$8^2 + 15^2 = 64 + 225 = 289$ , so the hypotenuse is $\sqrt{289} = 17$ .

Question 7easy

The hypotenuse of a right triangle is $25$ , and one leg is $7$ . Find the other leg.

$25^2 - 7^2 = 625 - 49 = 576$ , so the other leg is $\sqrt{576} = 24$ .

Question 8easy

The legs of a right triangle measure $7$ and $24$ . How long is the hypotenuse?

$7^2 + 24^2 = 49 + 576 = 625$ , so the hypotenuse is $\sqrt{625} = 25$ .

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