Question

Can the sides of a triangle be in the given ratio? 3:4:5

Answer 1

Answer:

Yes

Step-by-step explanation:

In order to determine if a triple of values will form a triangle, we must apply the Triangle Inequality Theorem, which states that for a triangle with lengths a, b, and c:

a + b > c

a + c > b

b + c > a

Here, let's suppose that since the ratio of the sides is 3 : 4 : 5, then let the actual side lengths be 3x, 4x, and 5x, where x is simply a real value.

With loss of generality, set a = 3x, b = 4x, and c = 5x. Plug these into the Triangle Inequality to check:

a + b > c  ⇒  3x + 4x  >?  5x  ⇒  7x > 5x  ⇒  This is true

a + c > b  ⇒  3x + 5x  >?  4x  ⇒  8x > 4x  ⇒  This is also true

b + c > a  ⇒  4x + 5x  >?  3x  ⇒  9x > 3x  ⇒  This is true

Since all three conditions are satisfied, we know that a true triangle can be formed given that the ratio of their sides is 3 : 4 : 5.

~ an aesthetics lover

Answer 2

Answer:

Yes

Step-by-step explanation:

Yes, and it’s a right triangle.

3²+4²=5²

9+16=25

25=25