Question

What is the value of x?
_____ Units​

Answer 1

`x=25`

Explanation:

The line QC makes:

`\triangle DQC\sim\triangle DBR`

Using the property of similar triangles:

`(DQ)/(BD) =(DC)/(DR) \\\\(40)/(40+24) =(x)/(x+15)\\`

Using cross multiplication method:

`40(x+15)=x(40+24)\\\\40(x+15)=x(64)\\\\40(x)+40(15)=64x\\\\40x+600=64x`

Subtracting '
`40x`' both the sides:

`64x-40x=600\\\\24x=600`

Dividing by '24' both sides:

`x=(600)/(24) \\\\x=25`

The value of 'x' in the figure is :
`x=25`