Is it true that a triangle with sides measuring 12, 16, and 20 is a right triangle?

Answer 1

yes, of course

we know that 3^2 + 4^2 = 5^2; that is, the triangle with sides 3,4 and 5 is a right triangle... in fact any multiples of the 3-tuple (3,4,5) such as (6,8,10), (9,12,15).... are also right triangles...since they satisfy the pythagores rule (a^2+b^2=c^2) ...

some more:

5, 12, 13 and its multiples
7, 24, 25 ....
9, 40, 41 ....

one interesting fact: in all such triangles, one side must be divisible by 5 (easy to prove it....if you know....)

observe also that 3^2 = 4 + 5, 5^2 = 12 + 13, 7^2 = 24 + 25... can you see a pattern?

Answer 2

Alicia:

A triangle with sides of 12, 16 and 20 is a right triangle. Look at the ratio between the sides, and you'll see that this is so.

12:16:20 is the same as 3:4:5 - by now, you probably know that a 3-4-5 triangle is a right triangle.

To tell if any triangle is a right triangle, use the Pythagorean theorem: if the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse), you have a right triangle.

Here 12 squared is 144 and 16 squared is 256.

144 plus 256 = 400, which happens to be the answer you get when you square the hypotenuse (20). (20 squared is 400).

Answer 3

Yep!!

And I have already done the math. In fact decades ago. Construction people sometimes need to establish square corners and physical squares are just too small. We use two triangles primarily. They are 3, 4, 5 and 6, 8, 10. It can be done in inches, feet, yards, rods, any linear measurement. 12, 16, 20 triangle also works. I just don't use it as often as the others.

BTW, Double the numbers on your triangle and do the math. I.E. 24, 32, 40. Now double them again. Interesting isn't it... I love geometry.

Answer 4

Yes, because 12^2 + 16^2 = 20^2.

Answer 5

All right triangles have sides where A squared + B squared = C squared....so do the math and find out.....does 12 squared + 16 squared = 20 squared?

Answer 6

Yes. If the square of the largest number equals the sum of the squares of the smaller numbers, then it's a right triangle. It's the pythagorean theorem.

Answer 7

Yes, because if you simplified or divided all the numbers by 4, you would get 3,4, and 5. Ad, if i remember correctly, those are the tree numbers of a right triangle.

Answer 8

A right triangle has a ninty degree angle. So, I don't think so.

Answer 9

yes

Answer 10

yes