The two rectangles above are similar. If a = 6 in, b = 11 in, and d = 22 in, what is the length of c?
A.
30 in
B.
10 in
C.
14 in
D.
12 in
In similar rectangles, the ratio of their corresponding sides are equal, so a/d = b/c. Substituting the known values, we get 6/22 = 11/c. Cross-multiplying gives 6c = 242, which simplifies to c = 242/6 = 40.33. However, this value is not listed in the answer choices, so it seems there was a mistake in the problem's setup. As it stands, none of the answer choices is correct.
To find the length of c, we can use the property of similar triangles, which states that corresponding sides of similar shapes are proportional.
In this case, we can set up the following proportion:
a/b = c/d
Substituting the given values:
6/11 = c/22
To solve for c, we can cross-multiply and solve for c:
6 * 22 = 11 * c
132 = 11c
Divide both sides by 11:
132/11 = c
c = 12 in
Therefore, the length of c is 12 in. Hence, the correct answer is (D) 12 in.
To find the length of c, we need to use the concept of similarity of rectangles. In similar figures, corresponding sides are in proportion.
Let's consider the sides a, b, and c of the first rectangle and the sides x, y, and d of the second rectangle. We know that the two rectangles are similar, so we can set up the following proportion:
a/b = x/d
Plugging in the values we have:
6/11 = x/22
Now we can solve for x by cross-multiplying:
11x = 6 * 22
11x = 132
Dividing both sides by 11:
x = 12
Therefore, the length of c is 12 inches, so the correct answer is D.