A rancher is building a fence around a rectangular grazing pasture. The pasture is 140 fee… — Armed Services Vocational Aptitude Battery (ASVAB)

A rancher is building a fence around a rectangular grazing pasture. The pasture is $140$ feet long and $70$ feet wide. If the rancher needs to leave a $10$ -foot wide opening for a gate, how many total feet of fencing material will be required?

Answer: 410 feet

Answer

410 feet

To find the total amount of fencing required, you first determine the perimeter of the rectangle, which is

140 + 140 + 70 + 70 = 420

feet. Because there is a

10

-foot gate that does not require fencing, you subtract

10

from the total perimeter, leaving

410

feet.

Step-by-Step Solution

Calculate the total perimeter of the rectangular pasture.

2 \times (140 + 70) = 420

feet.

The fence runs along the entire outer boundary of the pasture, which requires finding the perimeter of the rectangle.

Subtract the gate opening from the total perimeter.

420 - 10 = 410

feet.

The

10

-foot opening for the gate does not use fencing material, so it must be subtracted from the total.

Key Concept

Calculating perimeter of a rectangle and adjusting for gaps or openings.

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