A rectangular field is fenced in by using a river as one side. If $1,400$ m of fencing are used for the $240,000$ -m² field, find its dimensions. A) $300 \mathrm {~m} \times 800 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ B) $450 \mathrm {~m} \times 900 \mathrm {~m} , 400 \mathrm {~m} \times 650 \mathrm {~m}$ C) $300 \mathrm {~m} \times 800 \mathrm {~m} , 450 \mathrm {~m} \times 600 \mathrm {~m}$ D) $300 \mathrm {~m} \times 1,000 \mathrm {~m} , 400 \mathrm {~m} \times 600 \mathrm {~m}$ E) $200 \mathrm {~m} \times 700 \mathrm {~m} , 500 \mathrm {~m} \times 700 \mathrm {~m}$

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Quizplus · Accepted Answer

The area of the field is $240,000 \, \text{m}^2$, and the perimeter that needs fencing (excluding the river side) is $1,400 \, \text{m}$. For a rectangle, the area is $l \times w$ and the perimeter is $2(l + w)$, but since one side is the river, the fencing covers only $l + 2w = 1,400$. The dimensions that satisfy both the area and the fencing condition are $300 \, \text{m} \times 800 \, \text{m}$ and $400 \, \text{m} \times 600 \, \text{m}$.

A Rectangular Field Is Fenced in by Using a River 1,4001,4001,400

A Rectangular Field Is Fenced in by Using a River $1,400$