Do the lengths a=9, b=12, c=15 form a right triangle?

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Yes

Step-by-step explanation:

With a right angle triangle, there are 3 sides.

There is the hypotenuse, the longest side, which is always opposite to the right-angle.

There are then the two other sides, which are shorter.

By what is known as the pythagorean principle, the square of the hypotenuse (meaning its length squared) will equate to the sum of the squares of the other two sides.

So if we say the hypotenuse is, say, "c" cm long, and the other two sides are "a"  and "b" cm long, then we can write the pythagorean principle as an equation like so:

c² = a² + b²

Now that we have established this, we can answer the question asked.

the longest side is c, which is 15 cm, so this is the hypotenuse.

So, a and b are the other two sides.

Now we just plug the numbers into the equation, and see if the numbers on either side are the same:

(15)² = (9)² + (12)²

Well,

(15)² = 225,

(9)² = 81,

And,

(12)² = 144

So, Is:

225 = 144 + 81

Indeed, it is, therefore the triangle with sides of length 9, 12 and 15 cm is a right-angle triangle.

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step-by-step explanation:

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