A rectangle contains 324 sq cm. If the length is nine less than three times the width, what are the dimensions of the rectangle?
2 Answers
Explanation:
Explanation:
#"let the width "=w#
#"then length "l=3w-9to" 9 less than 3 times width"#
#"area of rectangle "="length"xx"width"#
#rArr"area "=w(3w-9)#
#"now area "=324" cm"^2#
#rArrw(3w-9)=324#
#"distribute and equate to zero"#
#rArr3w^2-9w-324=0larrcolor(blue)"in standard form"#
#rArr3(w^2-3w-108)=0#
#"factor "w^2-3w-108" using the a-c method"#
#"The factors of - 108 which sum to - 3 are - 12 and + 9"#
#rArr3(w-12)(w+9)=0#
#"equate each factor to zero and solve for w"#
#w-12=0rArrw=12#
#w+9=0rArrw=-9#
#"but "w>0rArrw=12#
#"Hence width "=w=12" cm and"#
#"length "=3w-9=(3xx12)-9=27" cm"#