The greatest whole number possible length for the given measures of triangle is 23 cm.
As given in the question,
Measure of two side-length of a given triangle are :
Let 'x' be the side length = 8.5cm
And 'y' be the side length = 15cm
'z' be the side length of the third side of a triangle.
Sum of two sides is greater than third side and difference of two sides is smaller than the third side.
y - x < z < y + x
⇒ 15 - 8.5 < z < 15 + 8.5
⇒ 6.5 cm < z < 23.5cm
Greatest whole number representing length of the third side of a triangle is less than 23.5 .
⇒ z = 23cm
Therefore, the length of the third side of a triangle represented by greatest whole number is equal 23cm.
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