Question

Triangle CDE is an isosceles triangle with CD = DE. If CD = 9x - 25, DE = 6x + 8, and CE = 10x - 73, find x and the measure of each side.

Answer 1

By setting the equations for the isosceles triangle's equal sides CD and DE, we find x=11. The side lengths of triangle CDE are CD = 74 units, DE = 74 units, and CE = 37 units.

Step-by-step explanation:

To find the value of x in the isosceles triangle CDE with sides CD = DE, we set the expressions for these sides equal to each other because in an isosceles triangle, at least two sides are the same length. Thus, we solve the equation 9x - 25 = 6x + 8 for x. After rearranging the terms, we get 3x = 33, leading to x = 11.

Substituting x back into the expressions given for each side, we find:

• CD = 9x - 25 = 9(11) - 25 = 74
• DE = 6x + 8 = 6(11) + 8 = 74 (which should be the same as CD)
• CE = 10x - 73 = 10(11) - 73 = 37

Therefore, the sides of the isosceles triangle CDE measure CD = 74 units, DE = 74 units, and CE = 37 units.