Answer
6 yd by 8 yd
Work Step by Step
Given Mary Frances has a rectangular garden plot that encloses an area of 48 $yd^{2}$. If 28 yd of fencing are purchased to enclose the garden,
Lets assume that the length of base of rectangle be b and the altitude has length h then area of rectangle A = bh
bh = 48$yd^{2}$
The perimeter of garden plot = fencing length
Perimeter of rectangle plot = 2(l+b) = 28 yd
As we know bh = 48
b = $\frac{48}{h}$
now put the value of b in perimeter equation
2( $\frac{48}{h}$ + h) = 28
$\frac{48 + h^{2}}{h}$ = 14
48 + $h^{2}$ = 14h
$h^{2}$ - 14h + 48 = 0
$h^{2}$ -8h - 6h +48 = 0
h(h-8)-6(h-8)=0
(h-6)(h-8)=0
h-6=0 or h-8=0
so h=6,8
using h =6 the value of b = $\frac{48}{6}$ = 8
using value h=8 the value of b = $\frac{48}{8}$ = 6
Therefore the dimensions of a rectangular plot is 8yd by 6 yd or 6yd by 8yd
