What is the length of AC

Answer:
Option A is correct.
The length of AC = 136 unit.
Explanation:
AA(Angle-Angle) similarity postulate states that two triangles are similar if they have two corresponding angles that are congruent or equal in measure.
First show that ΔBAC and ΔDEC are similar triangle.
In ΔBAC and ΔDEC
[tex]\angle BAC = \angle DEC = 90^{\circ}[/tex] [Angle] [Given in figure]
[tex]\angle BCA =\angle DCE[/tex] [Angle] [Given]
then, by AA postulates we can say that ;
[tex]\triangle BAC \sim \triangle DEC[/tex]
In similar triangle, their corresponding sides are in proportion.
Therefore, in ΔBAC and ΔDEC
[tex]\frac{AB}{DE}= \frac{AC}{CE}[/tex] ......[1]
from the figure, we have
AB = 51 unit , AC = 144-x unit , DE =3 unit and CE =x unit.
Substitute these in [1] to solve for x;
[tex]\frac{51}{3}= \frac{144-x}{x}[/tex]
Simplify:
[tex]17= \frac{144-x}{x}[/tex]
By cross multiply we get;
[tex]17x =144-x[/tex]
or
[tex]17x+x =144[/tex] or
18x =144
Divide both sides by 18 we get;
x = 8.
Then, the length of AC = 144-x =144-8 = 136 unit.