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Deondra has 57 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 340 square meters. List each set of possible dimensions
(length and width) of the field.

Respuesta :

(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.

 

Calculate the set of possible dimensions (length and width) of the field:

Let length be L and width be W.

Given that,

three sided fence has a length of 57m,

⇒ 2W + L = 57 m ⇒ L = 57 - 2W

the area of the land is 340 square meters

length × width = 340 ⇒ L × W = 340

(57 - 2W)W = 340

57W - 2W² = 340

2W² - 57W + 340 = 0

Solve for W using quadratic formula,

a = 2, b = -57, c = 340

W = (-b±√b²-4ac)/2a  

   = (57±√3249-2720)/4

   = (57±√529)/4

   = (57±23)/4

W = 20 m and W = 8.5 m  

For W=20, L=57-2(20) = 17

For W=8.5, L=57-2(8.5) = 40

Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.

Learn more about quadratic equations:

brainly.com/question/5975436

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