Question #1466c

1 Answer
Feb 8, 2017

x=28x=28

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=57/42x+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=42015x=420

rArrx=420/15=28x=42015=28