Question

Question #1466c

Answer 1

`x=28`

Explanation:

Triangle APR and triangle CDR are `color(blue)"similar"`

`rArr"the ratios of corresponding sides are equal"`

`color(blue)"Ratios of corresponding sides are"`

`(AP)/(CD)=(AR)/(CR)=(PR)/(DR)`

substitute in known values to the ratios.

`"Using " (AR)/(CR)=(PR)/(DR)`

`rArr(x+10)/x=(42+15)/42=57/42`

`rArrcolor(red)(x+10)/color(blue)(x)=color(blue)(57)/color(red)(42)`

`color(magenta)"cross multiplying"`

`rArrcolor(red)(42(x+10)=color(blue)(57x)`

distributing.

`42x+420=57x`

`rArr15x=420`

`rArrx=420/15=28`