Answer:
The value of x is 5.
Step-by-step explanation:
It is given that both triangles are similar.
In triangle ABC and DEC,
[tex]\angle ABC=\angle DEC[/tex] (Given)
[tex]\angle ACB=\angle DCE=90^{\circ}[/tex] (Given)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle DEC[/tex]
The corresponding sides of similar triangles are proportional.
[tex]\frac{AB}{DE}=\frac{BC}{EC}=\frac{AC}{DC}[/tex]
[tex]\frac{4x}{3x+1}=\frac{3+12}{12}[/tex]
[tex]12\times 4x=15\times (3x+1)[/tex]
[tex]48x=45x+15[/tex]
[tex]3x=15[/tex]
Divide both sides by 3.
[tex]x=5[/tex]
Therefore the value of x is 5.
