ANSWER
[tex]x = 3[/tex]
[tex]CD= 21 \: units[/tex]
[tex]DE= 16 \: units[/tex]
[tex]CE= 21 \: units[/tex]
EXPLANATION
It was given that ∆CDE is an isosceles triangle.
The length of the sides are given in terms of x as follows.
[tex]CD=4x+9[/tex]
[tex]DE=7x-5[/tex]
[tex]CE=16x-27[/tex]
It was also given that, angle D is congruent to angle E.
This implies that, side CD and CE are equal.
Thus,
[tex] |CD| = |CE| [/tex]
In terms of x, we have;
[tex]4x + 9 = 16x - 27[/tex]
We group like terms to get,
[tex]16x - 4x = 9 + 27[/tex]
[tex]12x = 36[/tex]
Divide both sides by 12 to get,
[tex]x = \frac{36}{12} [/tex]
[tex] \therefore \: x = 3[/tex]
The length of the sides are;
[tex]CD=4(3)+9 = 21 \: units[/tex]
[tex]DE=7(3)-5 = 16 \: units[/tex]
[tex]CE=16(3)-27 = 21 \: units[/tex]
