Question

Which of the following sets of lengths can Sean use to make a right triangle?

Answer 1

Answer:

{8 cm, 15 cm, 17 cm}

Step-by-step explanation:

we know that

The length sides of a right triangle must satisfy the Pythagoras 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

{5 cm, 15 cm, 18 cm}

substitute in the formula

$18^2=5^2+15^2$

$324=250$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 2) we have

{6 cm, 12 cm, 16 cm}

substitute in the formula

$16^2=8^2+12^2$

$256=208$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 3) we have

{5 cm, 13 cm, 15 cm}

substitute in the formula

$15^2=5^2+13^2$

$225=194$ ----> is not true

therefore

Sean cannot make a right triangle with this set of lengths

case 4) we have

{8 cm, 15 cm, 17 cm}

substitute in the formula

$17^2=8^2+15^2$

$289=289$ ----> is true

therefore

Sean can make a right triangle with this set of lengths