Question

Which of the following sets of numbers could represent the three sides of a right triangle?

Answer 1

Answer:

{39, 52, 65}

Step-by-step explanation:

The complete question is

Which of the following sets of numbers could represent the three sides of a right  triangle?

{44, 60, 75}

{30, 73, 78}

{37, 77,85}

{39, 52, 65}

we know that

The three sides of a right triangle must satisfy the Pythagorean Theorem

so

$c^2=a^2+b^2$

where

c is the greater side (the hypotenuse)

a and b are the legs (perpendicular sides)

Verify each case

case 1) we have

{44, 60, 75}

Let

$c=75\ units\\a=44\ units\\b=60\ units$

substitute

$75^2=44^2+60^2$

$5,625=5,536$ ----> is not true

so

The set of number  could not represent the three sides of a right triangle

case 2) we have

{30, 73, 78}

Let

$c=78\ units\\a=30\ units\\b=73\ units$

substitute

$78^2=30^2+73^2$

$6,084=6,229$ ----> is not true

so

The set of number  could not represent the three sides of a right triangle

case 3) we have

{37, 77,85}

Let

$c=85\ units\\a=37\ units\\b=77\ units$

substitute

$85^2=37^2+77^2$

$7,225=7,298$ ----> is not true

so

The set of number  could not represent the three sides of a right triangle

case 4) we have

{39, 52, 65}

Let

$c=65\ units\\a=39\ units\\b=52\ units$

substitute

$65^2=39^2+52^2$

$4,225=4,225$ ----> is true

so

The set of number  could represent the three sides of a right triangle