## The length of the edging that surrounds circular…

## Solution:

We are given that the length of edging that surrounds circular garden K is ½ the length of the edging that surrounds circular garden G. Since the gardens are circular, we know that the circumference of garden K is ½ the circumference of circular garden G. We will use the circumference formula C = 2[Symbol]r. If we let G = the radius of garden G, and K = the radius of garden K, we can create the following equation.

2[Symbol]K = ½(2[Symbol]G)

We need to determine the area of garden K, using the area formula A = [Symbol]r^2. Since K = the radius of garden K, we know:

Area of garden K = [Symbol]K^2

Thus, if we can determine the value of K, we can determine the area of garden K.

**Statement One Alone: **

The area of G is 25[Symbol] square meters.

We can use the information in statement one to determine the value of the radius of garden G.

25[Symbol] = [Symbol]G^2

25 = G^2

√25 = √G^2

5 = G

Since we have the value of G, we can determine the circumference of garden G.

circumference of garden G = 2[Symbol]G

circumference = 2[Symbol] x 5

circumference = 10[Symbol]

From the given information we also know that:

2[Symbol]K = ½(2[Symbol]G)

Since 10[Symbol] is the circumference of garden G, we can substitute 10[Symbol] for 2[Symbol]G in the equation 2[Symbol]K = ½(2[Symbol]G). We can now determine a value for K.

2[Symbol]K = ½(10[Symbol])

2[Symbol]K = 5[Symbol]

K = 2.5

Since the radius of garden K is 2.5, we have enough information to determine the area of garden K. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

The edging around G is 10[Symbol] meters long.

Using the information in statement two, we know that the circumference of garden G is 10[Symbol].

Recall that in statement one, we already determined that the circumference of garden G is 10[Symbol]. This is enough information to determine the radius of garden K and hence the area of garden K. Statement two alone is also sufficient to answer the question.

**Answer:** D