The perimeter of the rectangle with sides #8a+6# and #9a + 10# is 304 ft. What are the values of its sides?
1 Answer
Mar 29, 2018
Explanation:
#"the perimeter of a rectangle is"#
#•color(white)(x)"perimeter "=2l+2b#
#"where "l" is the length of one side and " b" the"#
#"length of the other side"#
#"let "l=9a+10" and "b=8a+6#
#rArr2l+2b=2(9a+10)+2(8a+6)#
#color(white)(xxxxxxx)=18a+20+16a+12#
#color(white)(xxxxxxx)=34a+32#
#"now perimeter "=304#
#rArr34a+32=304#
#"subtract 32 from both sides"#
#34acancel(+32)cancel(-32)=304-32#
#rArr34a=272#
#"divide both sides by 34"#
#(cancel(34) a)/cancel(34)=272/34#
#rArra=8#
#"one side "=(8xx8)+6=64+6=70" feet"#
#"other side "=(9xx8)+10=72+10=82" feet"#
#color(blue)"As a check"#
#"perimeter "=(2xx70)+(2xx82)=140+164=304" feet"#