Two sides of a triangle measures 4cm and 9cm determine which of the following choices cannot be the measures of the third side.
To determine which of the following choices cannot be the measure of the third side, we can apply the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's call the two given sides of the triangle "a" and "b", with lengths 4cm and 9cm respectively. We need to find the measure of the third side, which we will call "c".
Applying the triangle inequality theorem, we have:
a + b > c
Substituting the given lengths, we have:
4 + 9 > c
13 > c
Therefore, the measure of the third side "c" must be less than 13cm.
Now let's analyze the choices:
a) 10cm: This is a valid measure for the third side since it is less than 13cm.
b) 5cm: This is a valid measure for the third side since it is less than 13cm.
c) 12cm: This is a valid measure for the third side since it is less than 13cm.
d) 15cm: This is not a valid measure for the third side since it is equal to or greater than 13cm. It violates the triangle inequality theorem.
Therefore, the measure of 15cm cannot be the measure of the third side.