Question

A fence was build arpund a square yard. It took 500 feet² of lumber to build the fence. The fence is five feet tall. What is the area of the yard inside the fence?

Answer 1

625 square feet

Explanation:

The length of the fence is its area divided by its height:

A = LW

500 ft² = L(5 ft)

(500 ft²)/(5 ft) = 100 ft = L

This encloses a square, so the side of the square is 1/4 of this length:

side = (100 ft)/4 = 25 ft

The yard's area is the square of the length of its side dimension:

yard area = (25 ft)² = 625 ft²

The area of the yard inside the fence is 625 square feet.

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Comment on units

If you keep units with numbers, you know that dividing 500 ft² by 5 ft will give a measure of 100 ft. This is a linear measure, not an area measure, so tells you that this is not the answer to the question of yard area.