A rectangular garden has an area of 84 m² and a perimeter of 38 m. Find its length and width

Question

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Answer 1

you can get the answer without using quadratic equations, so first we'll get the answer using arithmetic and then using quadratic equations

38/2=19, half of the perimeter

84=2*2*3*7=(2*2*3)*(7)=12*7 and 12+7=19

length and width are 7 and 12 or 12 and 7 (meters)

P=2l+2w

38=2l+2w

19=l+w

l=19-w

A=lw

84=(19-w)w

84=19w-w²

w²-19w+84=0

factor

now, you factor 84 which is what I did at the top...

84=(2*2*3)*(7)

(w-12)(w-7)=0

w-12=0

w=12 (and l=7)

or,...

w-7=0

w=7 (and l=12)