Answer :
Final answer:
The question involves solving a quadratic equation to find the width of a concrete walk around a garden. The garden measures 10 m by 16 m, and the area of the walk is 120 m². By setting up an equation for the total area and factoring, the width of the walk is found to be 2 meters.
Explanation:
The question involves finding the uniform width of a concrete walk surrounding a rectangular garden. The garden measures 10 m by 16 m with the area of the walk being 120 m2. Let's call the width of the walk 'w'. The total area covered by the garden and the walk will be (10 + 2w) * (16 + 2w). Since we know the area of just the garden is 10 * 16 = 160 m2, we can find the total area by adding 120 m2 to it, resulting in 280 m2. Now we can set up the equation:
(10 + 2w) * (16 + 2w) = 280
To solve for 'w', expand the left side of the equation:
160 + 20w + 32w + 4w2 = 280
Combining like terms gives us:
4w2 + 52w + 160 = 280
Subtract 280 from both sides to set the equation to zero:
4w2 + 52w - 120 = 0
Divide everything by 4 to simplify:
w2 + 13w - 30 = 0
Factor the quadratic equation:
(w + 15)(w - 2) = 0
Therefore, we have two possible solutions for 'w': -15 and 2. Since a negative width is not possible for a walk, we discard -15 and are left with the width of the walk as 2 meters.
