lheiannie07 wrote:What is the perimeter of rectangle ABCD?
(1) The longer side of the rectangle is 2 meters shorter than its diagonal
$$(2)The\ ratio\ of\ the\ shorter\ side\ of\ the\ rec\tan gle\ to\ its\ diagonal\ is\ \frac{1}{3}\ $$
We need to determine the perimeter of rectangle ABCD.
Statement One Alone:
The longer side of the rectangle is 2 meters shorter than its diagonal.
We can let the length of the longer side = L and the length of the diagonal = G. Thus we have L = G - 2. However, since we don't know the value of L or G, we can't determine the perimeter of ABCD. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The ratio of the shorter side of the rectangle to its diagonal is 1/3.
We can let the length of the shorter side = W and the length of the diagonal = G. Thus we have W = G/3. However, since we don't know the value of W or G, we can't determine the perimeter of ABCD. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using the two statements, we see that L = G - 2 and W = G/3. Notice that the perimeter of ABCD is 2L + 2W. Furthermore, L, W and G form a right triangle with G as the hypotenuse. Thus, we have:
L^2 + W^2 = G^2
Now, substituting G - 2 for L and G/3 for W, we have:
(G - 2)^2 + (G/3)^2 = G^2
From the above equation, we can solve for G. Once we solve for G, we can determine the values of L and W and, hence, we can determine the perimeter of ABCD.
Answer:
C
