Question

A rectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?

Answer 1

• x = 1 m

Explanation:

Area of pool:

• 6*4= 24 m²

Area of walkway:

• (6+2x)(4 +2x) - 24 =
• 24 + 12x + 8x + 4x² - 24 =
• 4x² + 20x

If the areas are equal, then:

• 4x² + 20x = 24
• x² + 5x - 6 = 0
• x = (-5 ±√25+24)/2
• x = (-5 ± 7)/2
• x = 1 and
• x = -6 (excluded as negative)