Atriangle has sides lengths of 9 cm, 12 cm, and 15 cm. determine whether this is a right triangle and why.

Step-by-step explanation:

We can test these numbers to see if they satisfy the Pythagorean theorem equation:

  15² = 9² + 12²

  225 = 81 + 144 . . . . true

Since the numbers satisy the Pythagorean theorem relation, they belong to a right triangle.

You can recognize that the ratio of side lengths is ...

  9 : 12 : 15 = 3 : 4 : 5

Further, you can recognize that the side lengths 3, 4, 5 belong to the right triangle with the smallest integer side lengths that satisfy the Pythagorean theorem. Hence the 9 : 12 : 15 triangle is similar (by a scale factor of 3) to a right triangle, thus is a right triangle.

the answer to the expression is 83

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)