Answer :
Final answer:
The area of the walkway is 22 sq.m obtained by subtracting the garden's area from the total area. To express this as the sum of two terms, we calculate the width of the walkway and use it to determine the area of walkway along the length and width of the garden. The correct option is (a).
Explanation:
To find the area of the walkway, we first subtract the area of the garden from the total area (garden plus walkway). The area of the garden is given as 66 sq.m. The total area is 88 sq.m. Therefore, the area of the walkway is 88 sq.m - 66 sq.m = 22 sq.m.
Now, we need to express the area of the walkway as the sum of two terms from the given options. Since we have a boundary walkway, it has a uniform width all around the garden. If the original garden is 6.5m by 6.5m, adding equal widths (x) on all sides will result in new dimensions (6.5m + 2x) by (6.5m + 2x). Given that the area with the walkway is 88 sq.m, we can set up the equation:
(6.5m + 2x) * (6.5m + 2x) = 88 sq.m
Let's solve for x:
(6.5 + 2x)² = 88
(6.5 + 2x) * (6.5 + 2x) = 88
42.25 + 26x + 4x² = 88
4x² + 26x + 42.25 - 88 = 0
4x² + 26x - 45.75 = 0
Using the quadratic formula or factoring to solve for x will yield the width of the walkway. With the width determined, the area of walkway can be expressed as:
2 * (width of walkway) * length of garden + 2 * (width of walkway) * width of garden = 2x * 6.5m + 2x * 6.5m = 22 sq.m
