Which set of three numbers could represent the lengths of the sides of a right triangle? A. 7, 9, 11 B. 8, 15, 17 C. 10, 15, 20 D. 12, 18, 22

To answer this problem, we use the Pythagorean theorem which states that the square of the hypotenuse or the longest side is equal to the sum of the squares of the legs. Hence trying each option, we verify whether the dimensions are true to the right triangle theorem. In this case, the answer is B.

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lisboa lisboa · Answer 2 · 2022-02-01T13:39:41+01:00

Set of three numbers that represents the length of the sides of the right triangle is 8,15,17

Given :

When the length of the sides is a right triangle then it should satisfy Pythagorean theorem .

[tex]c^2=a^2+b^2[/tex]

the square of the hypotenuse is equal to the sum of the square of the sides of legs.

Lets check each option

A: 7,9,11

[tex]11^2=9^2+7^2\\121=81+49\\False[/tex]

B: 8,15,17

[tex]17^2=15^2+8^2\\289=225+64\\289=289 (true)[/tex]

These sides of the triangle satisfies Pythagorean theorem . So, it forms a right triangle.

C: 10,15,20

[tex]20^2=10^2+15^2\\400=100+225\\false[/tex]

D: 12,18,22

[tex]22^2=12^2+18^2\\484=144+324\\484=468[/tex]

false

So, 8, 15, 17 represents the length of the sides of the right triangle .

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