Question #1466c
1 Answer
Feb 8, 2017
Explanation:
Triangle APR and triangle CDR are
color(blue)"similar"similar
rArr"the ratios of corresponding sides are equal"⇒the ratios of corresponding sides are equal
color(blue)"Ratios of corresponding sides are"Ratios of corresponding sides are
(AP)/(CD)=(AR)/(CR)=(PR)/(DR)APCD=ARCR=PRDR substitute in known values to the ratios.
"Using " (AR)/(CR)=(PR)/(DR)Using ARCR=PRDR
rArr(x+10)/x=(42+15)/42=57/42⇒x+10x=42+1542=5742
rArrcolor(red)(x+10)/color(blue)(x)=color(blue)(57)/color(red)(42)⇒x+10x=5742
color(magenta)"cross multiplying"cross multiplying
rArrcolor(red)(42(x+10)=color(blue)(57x)⇒42(x+10)=57x distributing.
42x+420=57x42x+420=57x
rArr15x=420⇒15x=420
rArrx=420/15=28⇒x=42015=28