Can someone please help me with this word problem?

Question

A farmer has rectangular garden plot surrounded by 488 ft of fence. Find the dimensions of the garden if its area is 12180 sq ft.??

Answer 1

divide by 3 and you will get your answer. deminson is used only when it is being times by three and another number

Answer 2

The easiest way to solve this question is with simultaneous equations (a system of equations). We'll call the length of the plot "x" and the width of the plot "y." The perimeter is equal to 2x+2y and the area is equal to xy.

Since we're given the perimeter and area in terms of actual numbers, all that's left now is to set them equal to the expressions we came up with and solve the system.

2x+2y=488
xy=12,180

Dividing the first equation by 2 and the seecond equation by x, we get:

x+y=244
y=12,180/x

Solving for y in the first equation, we get:

y=244-x
y=12,180/x

Setting the two quantites equal to each other:

244-x=12,180/x

Multiply by -x and add 12,180 to both sides:

xSquared-244x+12,180=0

Plug this into the quadratic formula:

x=(244plus or minus Rad(59,536-4(1)(12,180)))/2

This equals (244 plus or minus 104)/2, which gives values of 174 and 70, the dimensions of the garden plot.

Answer 3

2L + 2W = 488
L x W = 12180
L = 12180/W

Substituting for 'L'

2(12180/W) + 2W = 488
24360/W + 2W = 488
24360 + 2W^2 = 488W
2W^2 - 488W + 24360 = 0 (Factorise)
2[w^2 - 244W + 12180] = 0

w = [--244 +/- sq rt(244^2 - 4(1)(12180))]/2(1)
w = [244 +/- sqrt(59536 - 48720)]/2
w = [244 +/- sq rt(10816)]/2
w = [244 +/- 104]/2
w = 348/2 = 174
&
w = 140/2 = 70

So width is either 70 ft or 174 ft
But you will find the length results in same values
So Length = 174 ft and Width = 70 ft.

Answer 4

let x and y be the length and the widths

Area = width * length
Perimeter = 2 (width + length)

12,190 = xy
488 = 2(x + y)

solve
x = 12,180/y

488 = 2(12,180/y + y)
244 = 12,180/y + y
244y = 12,180 + y^2
0 = y^2 - 244y + 12,180

use quadratic formula and you'll get y = 70 and147

x = 12,180 / 70
x = 147

x = 12,180/147
x = 70

so the demention is 70ft x 147ft

hope this helps

Answer 5

70 wide and 174 long

Answer 6

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Answer 7

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