A rectangle contains 324 sq cm. If the length is nine less than three times the width, what are the dimensions of the rectangle?

Answer 1

#"length "=27" cm and width "=12" cm"#

#"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"#
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Answer 2

#l=27cm#
#w=12cm#

#l="length"# #w="width"#
#l=3*w-9# #A=color(red)(l)*w# #A=color(red)((3*w-9))*w# #324=3w^2-9w|:3# #108=w^2-3w|-108# #0=w^2-3w-108# #0=(w-3/2)^2-108-9/4|+441/4# #441/4=(w-3/2)^2|sqrt()# #+-21/2=w-3/2|+3/2# #3/2+-21/2=w# #w_1=12cm or cancel(w_2=-9cm)#
#l=3*12-9=27cm#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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