# Dimensions of the Lot for a Given Cost of Fencing

Date of Exam:

**Problem**

A rectangular waterfront lot has a perimeter of 1000 feet. To create a sense of privacy, the lot owner decides to fence along three sides excluding the sides that fronts the water. An expensive fencing along the lot’s front length costs Php25 per foot, and an inexpensive fencing along two side widths costs only Php5 per foot. The total cost of the fencing along all three sides comes to Php9500. What is the lot’s dimensions?

A. 300 feet by 100 feet | C. 400 feet by 200 feet |

B. 400 feet by 100 feet | D. 300 feet by 200 feet |

**Answer Key**

[ D ]

**Solution**

Let the dimension of the rectangular lot be

*x*and*y**x*= sides parallel to water*y*= sides perpendicular to waterPerimeter

$2x + 2y = 1000$

$x + y = 500$ ← Eq. (1)

Cost of fence

$25x + 5(2y) = 9500$

$5x + 2y = 1900$ ← Eq. (2)

Equation 2 - 2 × Equation (1)

$3x = 900$

$x = 300 ~ \text{ft}$

From Equation (1)

$300 + y = 500$

$y = 200 ~ \text{ft}$

Answer = 300 ft × 200 ft → [ D ]

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