Answer
the dimensions of the garden is $ 100m$ by $50m$
Work Step by Step
Given:
$P=300m$ (based on the enclosed fencing)
$A=5000m^{2}$
$L=150-x$
$W=x$
Remember the formula for perimeter and area:
$P = 2(L+W)$
$300 = 2(L+W)$
$A = L×W$
$5000 = L×W$
Substitute the given value of L to the area equation
$5000 = L×W$
$5000 = (150-W)×W$
Simplify by factoring
$5000 = 150W-W{2}$
$W^{2} -150W+5000 = 0 $
$(W-100)(W-50) = 0$
So $W = 100$ or $W = 50$
Since we already found the value of W. Now it's time to solve for L.
$L = 150 - W$
if W = 50m
$L = 100m$
if W = 100m
$L = 50m$
So the dimensions of the garden is $100m$ by $50m$.
