# 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"#