Two sides of scalene triangle ABC measure 3 centimeters and 5 centimeters. How many different whole centimeter lengths are possible for the third side?
By the triangle inequality, only 3,4,5,6,7 fulfill 3+x>5 and 5+3>x. However, it is scalene, so 3 and 5 do not work, leaving 3 possibilities.So the answer is 3.
Must be less than 3+5 and more than 5-3
2 sides
I know it is not 7.
So it must be 3, 4, 5, or 6.
p.athri, what do you mean by 2 sides?
To find the possible whole centimeter lengths for the third side of the triangle, we need to use the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must always be greater than the length of the third side.
In this case, let's consider the two known sides: one measuring 3 centimeters and the other measuring 5 centimeters. To find the possible lengths for the third side, we need to find the range of values that satisfy the triangle inequality.
Using the triangle inequality theorem, we can write the following inequality:
3 + 5 > x,
where x is the length of the unknown third side.
By solving the inequality, we get:
8 > x,
which means the third side must be less than 8 centimeters.
Since we want to find the possible whole centimeter lengths, we can conclude that the possible lengths for the third side are 1, 2, 3, 4, 5, 6, and 7 centimeters. Therefore, there are 7 different whole centimeter lengths that are possible for the third side of the triangle.