Question

A community garden offers two different square-shaped plots of growing space. The larger plot measures one square meter greater than the smaller one. The combined lengths of the two gardens is 3+2 radical 2 meters. What is the area of garden 1?

Answer 1

3 + 2√(2)

Explanation:

Since the larger plot is 1²m greater than the smaller one.

Let x denote the length of the smaller one, this implies that the larger would be x + 1.

Since the combined length is 3 + 2√(2) we have:

x + (x + 1) = 3 + 2√(2)

2x + 1 = 3 + 2√(2)

2x = 2 + 2√(2)

x = 1 + √(2)

This is the length of the smaller plot. It's area would therefore be:

x² = [1 + √(2)]² = 1 + 2√(2) + 2 = 3 + 2√(2)