Question

A triangle has sides with lengths of 6 inches, 8 inches, and 11 inches. Is it a right triangle

Answer 1

Answer:

No

Step-by-step explanation:

In every right triangle, $a^{2} +b^2=c^2$ where "a" and "b" are the legs of the right triangle and "c" is the hypotenuse (This is known as "Pythagorean's theorem). To figure out if a triangle with side lengths 6, 8, and 11 inches is a right triangle, all you have to do is plug in the values 6 and 8 for "a" and "b" and the value 11 for "c" to get":

$6^2+8^2=11^2$

This simplifies to:

$36+64=121$

Which simplifies further to:

$100=121$

This is obviously incorrect so therefore, the triangle lengths given do not form a right triangle.

Hope this helps :)

Answer 2

Answer:

NO.

Step-by-step explanation:

If it is a right triangle then if h = longest side then by the inverse of Pythagoras Theorem:

h^2 = a^2 + b^2     (where a and b are other 2 sides).

So with the given values:

h^2 = 11^2 = 121

a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100.

-not equal so NOT a right triangle.