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
[tex]c^2=a^2+b^2[/tex]
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
[tex]18^2=5^2+15^2[/tex]
[tex]324=250[/tex] ----> 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
[tex]16^2=8^2+12^2[/tex]
[tex]256=208[/tex] ----> 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
[tex]15^2=5^2+13^2[/tex]
[tex]225=194[/tex] ----> 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
[tex]17^2=8^2+15^2[/tex]
[tex]289=289[/tex] ----> is true
therefore
Sean can make a right triangle with this set of lengths
