Question

If a triangle has side lengths 7, 10, and 12, is it a right triangle??

Answer 1

Answer:

No. Remember, a right angle must have a 90 degree angle. We can find the lengths with the Pythagorean Theorem.

Step-by-step explanation:

Given the length 7, 10, and 12, we can assume that 12 is the hypotenuse (it is the longest length).

- we can use 7 and 10 interchangeably.

Fill in the equation, $a^2 + b^2 = c^2$

                 where c = 12, and a or b = 7 or 10.

To indicate if the given lengths would form a right angle, we can only input 7 or 10, not both.

Therefore, $7^2 + b^2 = 12^2$ or $10^2 + b^2 = 12^2$

$7^2 + b^2 = 12^2$ ==> 49 + b^2 = 144 ==> b= $\sqrt{95$ ==> 9.746

b= 9.7, not 10.

$10^2 + b^2 = 12^2$ ==> 100 + b^2 = 144 ==> b = $\sqrt{44$ ==> 6.633

b= 6.6, not 7.

Therefore, the lengths 7, 10, and 12, does NOT make a right triangle.

Hope this helps!