A rectangular parking lot has a perimeter of 200 yards. The length of the parking lot is 4… — Armed Services Vocational Aptitude Battery (ASVAB)

A rectangular parking lot has a perimeter of $200$ yards. The length of the parking lot is $40$ yards greater than its width. What is the area of the parking lot, in square yards?

Answer: 2100 sq yd

Answer

2100

The correct answer is derived by first finding the individual dimensions using the perimeter formula and the given relationship (

l = w + 40

), which gives a width of 30 yards and a length of 70 yards. Multiplying these dimensions yields an area of 2100 square yards.

Step-by-Step Solution

Write the perimeter formula for a rectangle.

P = 2l + 2w

The perimeter is the total distance around the rectangle.

Translate the given information into equations.

2l + 2w = 200

and

l = w + 40

The problem states the perimeter is 200 yards and the length is 40 yards greater than the width.

Substitute the expression for length into the perimeter equation and solve for width.

2(w + 40) + 2w = 200 \Rightarrow 2w + 80 + 2w = 200 \Rightarrow 4w = 120 \Rightarrow w = 30

Substitution allows us to create an equation with only one variable.

Calculate the length.

l = 30 + 40 = 70

Now that we know the width is 30 yards, we can add 40 to find the length.

Calculate the area of the rectangle.

Area = l \times w = 70 \times 30 = 2100

The area of a rectangle is found by multiplying its length by its width.

Key Concept

Using algebraic equations to find the dimensions of a rectangle from its perimeter, and then calculating its area.

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