Answer:
[tex]x=25[/tex]
Step-by-step explanation:
The line QC makes:
[tex]\triangle DQC\sim\triangle DBR[/tex]
Using the property of similar triangles:
[tex]\dfrac{DQ}{BD} =\dfrac{DC}{DR} \\\\\dfrac{40}{40+24} =\dfrac{x}{x+15}\\[/tex]
Using cross multiplication method:
[tex]40(x+15)=x(40+24)\\\\40(x+15)=x(64)\\\\40(x)+40(15)=64x\\\\40x+600=64x[/tex]
Subtracting '[tex]40x[/tex]' both the sides:
[tex]64x-40x=600\\\\24x=600[/tex]
Dividing by '24' both sides:
[tex]x=\dfrac{600}{24} \\\\x=25[/tex]
The value of 'x' in the figure is : [tex]x=25[/tex]
