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

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

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Answer 1 · 2018-03-13T18:17:24

$l=27cm$
$w=12cm$

Explanation:

$l="length"$
$w="width"$

$l=3*w-9$
$A=color(red)(l)*w$
$A=color(red)((3*w-9))*w$
$324=3w^2-9w|:3$
$108=w^2-3w|-108$
$0=w^2-3w-108$
$0=(w-3/2)^2-108-9/4|+441/4$
$441/4=(w-3/2)^2|sqrt()$
$+-21/2=w-3/2|+3/2$
$3/2+-21/2=w$
$w_1=12cm or cancel(w_2=-9cm)$

$l=3*12-9=27cm$

Answer 2 · 2018-03-13T18:24:29

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

Explanation:

$"let the width "=w$

$"then length "l=3w-9to" 9 less than 3 times width"$

$"area of rectangle "="length"xx"width"$

$rArr"area "=w(3w-9)$

$"now area "=324" cm"^2$

$rArrw(3w-9)=324$

$"distribute and equate to zero"$

$rArr3w^2-9w-324=0larrcolor(blue)"in standard form"$

$rArr3(w^2-3w-108)=0$

$"factor "w^2-3w-108" using the a-c method"$

$"The factors of - 108 which sum to - 3 are - 12 and + 9"$

$rArr3(w-12)(w+9)=0$

$"equate each factor to zero and solve for w"$

$w-12=0rArrw=12$

$w+9=0rArrw=-9$

$"but "w>0rArrw=12$

$"Hence width "=w=12" cm and"$

$"length "=3w-9=(3xx12)-9=27" cm"$

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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

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