Question

Which of the following sets of numbers could represent the three sides of a righttriangle?{54, 72, 91} {5, 12, 14) {20, 22, 29} {48, 64, 80}

Answer 1

To answer this question, we can use the Pythagorean Theorem in each case to determine if each of the sides represents a side of a right triangle.

$h^2=a^2+b^2$

This is the algebraic expression of the Pythagorean Theorem. The hypotenuse is the largest side of the triangle.

First case

{54, 72, 91}

Hypotenuse = 91

Then, we have:

$91^2=54^2+72^2\Rightarrow8281=2916+5184\Rightarrow8281\ne8100$

They do not represent the sides of a right triangle.

Second case

{5, 12, 14)

Hypotenuse = 14

$14^2=5^2+12^2\Rightarrow196=25+144\Rightarrow196\ne169$

They do not represent the sides of a right triangle.

Third case

{20, 22, 29}

$29^2=20^2+22^2\Rightarrow841=400+484\Rightarrow841\ne884$

They do not represent the sides of a right triangle.

Fourth case

{48, 64, 80}

$80^2=48^2+64^2\Rightarrow6400=2304+4096\Rightarrow6400=6400$

This triple represents the sides of a right triangle.

In summary, the answer is {48, 64, 80} (last option).