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In the adjoining figure if a= 18 , b= 12...

In the adjoining figure if a= 18 , b= 12,c = 14 and d=8 , what is the measure of x?

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we have
`(PR)/(QR)= 12/18 = 2/3`
`(SR)/(PR) = 8/12 = 2/3`
Now in `trianglePRS and triangleQRP`
since , ` (PR)/(QR)= (SR)/(PR)` [ from (1) and (2) ]
and `angleR = angleR` (common)
(SAS similarity)
`(PR)/(QR)= (SR)/(PR)=(PS)/(QP)` ( corresponding sides of similar triangles are proportional)
`Rightarrow 2/3= 2/3 = x/14`
`Rightarrow x/14 = 2/3 Rightarrow x= 28/3`
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