Which of the following can be the ratio of the lengths of sides of a triangle: 4: 7: 8 and 3: 8: 13?Celia measured the angles and the lengths of...

The given ratios are as
follows:

4: 7: 8 and 3: 8:
13

The second ratio 3:8:13 given is not of sides as 3+8
< 13.

The reason is as
follows:

In a triangle, the sum of the lengths of any two
sides is greater than the 3rd side.

So even ratio of
sides of the triangle should make a similar triangle. Therefore, by above consideration,
if 3, 8 and 13 were the sides of a triangle, they do not obey the rule that the sum
of any two sides > greater than the 3rd
side.

Therefore 3:8:13 is not the ratio of
sides:

Therefore 4: 7: 8 may be the ratio of
the sides:

But even this does not pass the
test of sine rule as shown below:

So we do the
sine rule test.

Put a = 4, b=
7, c = 8 .

A= 180*3/(3+8+13) = 22.5
deg

B =180*/(3+8+13) = 60
deg

C = 180*13/(3+8+13) = 97.5
deg

A/sinA = b/sinB =
c/sinC.

4/sin22.5 =
10.4525.

7/sin60 =
8.08.

13/sin97.5 = 8.07.