Final answer:
After setting the expressions for the sides CD and DE of the isosceles triangle ACDE equal to each other, we solve for 'x' and find it to be 11. Using this value, we calculate the lengths of the sides, with CD and DE being 74 units and CE being 37 units.
Step-by-step explanation:
Finding the Value of 'x' in an Isosceles Triangle
An isosceles triangle has at least two sides that are equal in length. In this problem, the isosceles triangle ACDE has sides CD and DE that are equal. Given CD = 9x - 25, DE = 6x + 8, and CE = 10x - 73, we can find the value of 'x' by setting the expressions for CD and DE equal to each other and solving for 'x':
9x - 25 = 6x + 8
Grouping like terms gives us:
9x - 6x = 8 + 25
3x = 33
So,
x = 33 / 3
x = 11
Now, we can find the measure of each side:
CD = 9x - 25 = 9(11) - 25 = 99 - 25 = 74
DE = 6x + 8 = 6(11) + 8 = 66 + 8 = 74
CE = 10x - 73 = 10(11) - 73 = 110 - 73 = 37
Therefore, the measures of the sides are CD = DE = 74 and CE = 37.