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Just use the Pythagorean Theorem. A^2+B^2=C^2. Let the shortest side be have length A=x. Then the next shortest is B=(x+3), and the hypotenuse is C=(x+6). Insert these into the equation, and solve for x. You will get x=9 (or, x=-3, which you can throw out, because it doesn't make sense). So, the three side lengths are 9 cm, 12 cm, and 15 cm

Q: The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 3cm The difference between the lengths of the two perpendicular sidesis3cm3lengths?

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It is the angle opposite the hypotenuse which measures 90 degrees

The hypotenuse. It is used to measure height. Very simple equation.

Yes. If it is a right triangle, the angle opposite the hypotenuse will be right, 90o, therefore if the lines forming the angle were to continue, they would be perpendicular. What's the question?

The 2 sides perpendicular to its right angle

Circumcenter, this is the center-point of a circle circumscribed around the triangle. If the triangle is obtuse, then this point is outside the triangle and if the triangle is a right triangle, then the point is the midpoint of the hypotenuse.

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The perpendicular sides of a right triangle are its legs. The remaining side is the hypotenuse.

No but a right angle triangle has perpendicular sides and an hypotenuse.

I do believe you mean RIGHT triangle when you said perpendicular triangle. A right triangle has two legs and a hypotenuse. The area of a right triangle is 1/2 * (first leg) * (second leg) How do you determine which ones are the legs and which one is the hypotenuse? The hypotenuse is ALWAYS the largest number. So, choose the 2 smallest numbers.

Only at the midpoint of the hypotenuse.

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Because it is the sum of square of base and perpendicular

It is the angle opposite the hypotenuse which measures 90 degrees

The hypotenuse. It is used to measure height. Very simple equation.

Yes. If it is a right triangle, the angle opposite the hypotenuse will be right, 90o, therefore if the lines forming the angle were to continue, they would be perpendicular. What's the question?

The 2 sides perpendicular to its right angle

True, because the slant height and the altitude, or height, of the pyramid form one leg and the hypotenuse of a triangle withing the pyramid, and the hypotenuse of a triangle is always the longest side- it is not possible for the hypotenuse to be equal to the legs of a right triangle. (It is a right triangle because an altitude is perpendicular to the base of a pyramid.)

Circumcenter, this is the center-point of a circle circumscribed around the triangle. If the triangle is obtuse, then this point is outside the triangle and if the triangle is a right triangle, then the point is the midpoint of the hypotenuse.