Question

A triangle has side lengths of 8 8 inches, 12 12 inches, and 16 16 inches. Determine whether this is a right triangle and why. CLEAR CHECK No, because 8‾√+12‾‾‾√ 8 + 12 is not equal to 16‾‾‾√ 16 . Yes, because 8‾√+12‾‾‾√ 8 + 12 is equal to 16‾‾‾√ 16 . No, because 82+122 8 2 + 12 2 is not equal to 162 16 2 . Yes, because 82+122 8 2 + 12 2 is equal to 162 16 2 .

Answer 1

Answer:

It is not a right triangle

Step-by-step explanation:

A triangle has side lengths of 8 inches, 12 inches, and 16 inches.

To determine if it is a Right Triangle, we make use of the Pythagoras Theorem, i.e.

$Hypotenuse^2=Opposite^2+Adjacent^2$

Now the Hypotenuse is always the longest side

$16^{2} =8^2+12^2\\256=64+144\\256=208$

The equality above is not true and in fact

$256\neq 208$

Therefore the 3 numbers do not satisfy Pythagoras theorem and cannot be the lengths of a right triangle.

Answer 2

Answer:

A triangle has side lengths of 8

8

inches, 12

12

inches, and 16

16

inches.

Determine whether this is a right triangle and why.

CLEAR  CHECK

No, because 8‾√+12‾‾‾√

8

+

12

is not equal to 16‾‾‾√

16

.

Yes, because 8‾√+12‾‾‾√

8

+

12

is equal to 16‾‾‾√

16

.

No, because 82+122

8

2

+

12

2

is not equal to 162

16

2

.

Yes, because 82+122

8

2

+

12

2

is equal to 162

16

2

.

Step-by-step explanation: