MATHS HELP PLEASE! :)

A farmer uses 60m of fencing to make three sides of a rectangle sheep pen.The fourth side of the pen is a wall.Work out the length of the shorter sides of the pen if the area enclosed is 448m squared.

Please explain it to me! :)

Thank you!

P=2*x + 2*y (P = perimeter of rectangle (pen))
I P-y=2*x+y=60 (since one side is missing)
II A=x*y=448 (Area of rectangle (pen))

(transpose I)
I y=60-2x

(transpose II)
II y=448/x

connect through y (y=60-2x=448/x) :

448/x=60-2x

transpose
448=60x-2x^2

2x^2-60x+448=0 (divide by 2)
x^2 -30x + 224 = 0

this is a quadratic equation(how to solve this is linked)

x1=14
x2=16

now we can determine y1 and y2 through formula II.
y1=448/14=32
y2=448/16=28

test with x1|y1 on formula I: 14*2+32=60
ok
test with x2|y2 on formula I: 16*2+28=60
ok

so the answer would be:
The shorter sides of the pen are both either 14m or 16m long.

Maybe the dimensions are

30m x 15m

Total area is 450m (close enough?)

and the 60m was split into 15m (for each shorter side) and 30m for the longest side

Length of the shorter sides of the pen would be 15m.

i would just play with the numbers.