# Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 361: 31

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

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