Question

margo has 24 meters of wood to build a fence around her garden.She wants to create the largest area possible.Which dimensions will give margo the largest area

Answer 1

The rectangular dimension will give margo the largest area.

Step-by-step explanation:

Margo has 24 meters of wood to build a fence around her garden.She wants to create the largest area possible.

The rectangular dimension will give margo the largest area.

Hence, the rectangular dimension will give margo the largest area.

Answer 2

The largest possible area is in the shape of the square.

Step-by-step explanation:

let the length  be L and the width be W

margo has 24 meters of wood to build a fence around her garden.She wants to create the largest area possible

so the perimeter equation is

2L + 2W = 24

2(L+W) = 24

L+ W= 12

L= 12-W

to find the largest area

area = L×W

area = (12-W) ×W

area= 12W- W²

area equation is a quadratic, and I'm supposed to find the maximum. So all I really need to do is find the vertex. Since the above area equation is a negative quadratic, then it graphs as an upside-down parabola, so the vertex is the maximum.

A= -W²+ 12W

the vertex of the parabola is the point(h,k) where h= $\frac{-b}{2a}$

$h= \frac{-(12)}{2(-1)}$ = 6

to find the k part

k= (-6)² + 12(6)= 108 m²

the largest possible are is  108 m²

putting the value of W  in

L= 12-W

L= 12-6 = 6m

since the length and width is same 6m by 6 m

therefore ,

The largest possible area is in the shape of the square.

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