Find what the width and lengths are

Question

A sheep pen has and area of 90 m squared. someone divides the pen into two smaller pens with a length of fence. The total length of fence used is 48 m. What are the dimensions of the fence

Answer 1

assuming the pen is a rectangle, draw a rectangle and draw a vertical line inside the rectangle  from top to bottom parallel to the two sides; this divides the pen into two smaller pens

call the horizontal lines the lengths and call the vertical lines the widths

48=2l+3w

divide all terms by 2

24=l+1.5w

l=24-1.5w

A=lw

90=(24-1.5w)w

90=24w-1.5w²

1.5w²-24w+90=0

multiply all terms by 2

3w²-48w+180=0

divide all terms by 3

w²-16w+60=0

factor

(w-10)(w-6)=0

w-10=0

w=10 m

therefore l=9 m

90=9*10 and 3*10+2*9=30+18=48

w-6=0

w=6 m

therefore l=15 m

90=6*15 and 3*6+2*15=18+30=48

there are two answers: l=9 m and w=10 m and l=15 m and w=6 m