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Area and Perimeter?

Three sides of a fence an an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let x be the length of two sides perpendicular to the wall as shown. Write an equation of area A of the enclosure as a function of the lentgth x of the rectangular area as shown in the above figure. Then find value (s) of x for which the area is 5500 sq ft?

The square feet is confusing me the most; I don’t know how to convert it to regular feet.

Top 3 Answers
Anonymous

Favorite Answer

You cannot convert square feet, which measure an area, to feet, which measure a length.

If x ft. is the length of each of the two sides of the fence perpendicular to the wall, then the length of the third side is:

240 – 2x ft.

The area A (sq. ft) is the length multiplied by the width:

A = x(240 – 2x)

Therefore:

x(240 – 2x) = 5500

Extract the common factor of 2 on the LHS:

2x(120 – x) = 5500

x(120 – x) = 2750

Multiply out and subtract 2750:

120x – x^2 – 2750 = 0

x^2 – 120x + 2750 = 0

x = ( 120 +/- sqrt(120^2 – 4*2750) ) / 2

= 60 +/- 29.15

x = 89.15 or 30.85 ft.

2

    
let y be the length that is opposite of the wall

P = y + x + x

240 = y + 2x

Area formula

Area = w * L

Area = y * x

solve y:

y = 240 – 2x

Area = x (240 – 2x)

Area = -2x^2 + 240x

we want the area to be 5500 ft^2

5500 = -2x^2 + 240x

0 = -2x^2 + 240x – 5500

use quadratic formula and you’ll get:

x = 30.845ft or 89.154ft

1

Redsox324
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