Question

What is the value of x?



Enter your answer in the box.

Answer 1

ΔDCQ and ΔDRB are similar triangles thus the corresponding sides of the triangles have the same proportion.

Make a comparison of the corresponding sides

`(DC)/(DR)= (DQ)/(DB)`

plug in the numbers to the comparison above

`(DC)/(DR)= (DQ)/(DB)`

`(x)/(x+18)= (39)/(39 + 26)`

simplify the equation

`(x)/(x+18)= (39)/(39 + 26)`

`(x)/(x+18)= (39)/(65)`
simplify 39 and 65 by dividing them by 13

`(x)/(x+18)= (3)/(5)`

Do cross multiplication

`(x)/(x+18)= (3)/(5)`

`5x=3(x+18)`

Solve the equation
5x = 3(x + 18)
5x = 3x + 54
5x - 3x = 54
2x = 54
x = 54/2
x = 27

The value of x

`\boxed{\boxed{x=27}}`