Atriangle has two sides that measure 5 cm and 7 cm. which of the following cannot be the measure of the third side?
a 3 cm
b 10 cm
c 17 cm

Option C.

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

so

Let

c------> the length of the third side

case 1)

case 2)

------> rewrite

The solution of the third side is the interval------->

therefore

can not be a measure of the third side

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step-by-step explanation:

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this