Given that 2 sides of a triangle are 20 & 66. Find the range of possible measures for the third side, S.?

Question

Is It:

20< s <66

46 < s < 86

20 < s < 86

46 < s < 66

Answer 1

the sum of two sides of a triangle is greater than the third side.
20+66 > s
s < 86
and also 20+s > 66 => s > 46
and s+66 > 20 => s > -46

So combining 46 < s < 86

Answer is b

Answer 2

The third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.


From the triangle inequality, we know that c – b < a < c + b. The exact length of side a depends on the measure of the angle created by sides b and c. If this angle is large (close to 180º), then a will be large (close to b + c). If this angle is small (close to 0º), then a will be small (close to b – c).

66-20 The exact value of s depends on the measure of the angle opposite side s.

Answer 3

The triangle inequality demands that the sum of any 2 factors would desire to be extra desirable than the third area. you have 2 factors 5 and 13 with x being the third area. The triangle inequality demands that: 5+x > 13 ==> x > 8 5+13 > x ==> x < 18 13+x > 5 ==> authentic for any value of x > 0 The third area of triangle may well be everywhere between 8 and 18 inches

Answer 4

No one side can be longer than the sum of the other two sides.

If s is not the longest side:

66 < 20 + s
46 < s

If s is the longest side:

s < 20 + 66
s < 86

Putting these two together we have:

46 < s < 86

Answer 5

46 < s < 86

You can prove it basing on the statement the others have already said or, if you want to feel sure about that, use the cosine theorem, isolate the side you want to obtain and apply limit for ANGLE --> 0º (the smallest angle possible ==> shortest side), and for ANGLE --> 180º (the biggest angle possible ==> longest side), and you'll get 46 and 86 respectively ^^.

Answer 6

46
The rule: The sum of two sides of a triangle will always be MORE THAN the remaining side.