Respuesta :
Hello There!
To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.
Let's Test It!
"9+12=21" 21 is greater than 15
"9+15=24" 24 is greater than 12
Yes This Does Form A Triangle!
Answer:
Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.
Step-by-step explanation:
There are multiple different ways to prove that this answer is correct.
To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.
3x3=9
4x3=12
5x3=15
Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.
If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.
In this case, we get
9^2 + 12*2 = 15^2
If we simplify, we get:
81+144 = 225
And if simplified further, we get:
225=225,
Which is a true statement, proving that these side lengths do make up a right triangle.
Hope this helps!
