Question

Luke has 58 m of fencing to build a four -sided fence around a rectangular plot of land. The area of the land is 208 square meters. Solve for the dimensions (length and width ) of the field.The dimensions are __ meters by ___ meters

Answer 1

The dimensions are 16 meters by 13 meters.

Let x = length of the rectangular plot of land

y = width of the rectangular plot of land

If the area of the land is 208 square meters, then

A = xy

208 square meters =  xy

x = 208/y

If Luke has 58 m of fencing to build a four -sided fence around a rectangular plot of land, then the perimeter is the amount of fencing.

P = 2x + 2y

58 = 2(208/y) + 2y

58 = 416/y + 2y

58y = 416 + 2y²

2y² - 58y + 416 = 0

y² - 29y + 208 = 0

(y - 16)(y - 13) = 0

y = 16 ; y = 13

x = 208/16 = 13 ; x = 208/13 = 16

Since the length is usually longer than the width, then the dimensions are 16m long by 13m wide.

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