Problem Solving

answer is 9 underroot 2 i.e choice A . please explain how

Hi
The problem has given two hints, one is area of picture is equal to the area of frame ie; 18*15 - xy = xy

Assume x as length and y as width of the picture (of rectangle inside)

the second hint is equal ratios; 18/15 = x / y

solve these 2, we get the answer 9 sqrt 2.

Hope this clarifies ur question.

Ramana

If you don't know how to solve this one, you could also use an educated guess.

If the total area is 280, this means that the area of the picture is half that, 140.

The ratios are also equal:

18/15 = L/W

What two numbers do you need to multiply together in order to get an answer of 140. Just looking at the problem, you know that your answer will have a radical in it, because 18/15 reduces to 6/5 which does not give you a 140. I would guess that the answer will fall somewhere between 8 and 10.

B. 3/2 is too small of a length, leaving the width to be longer than the width of the frame. Eliminate.

C. 9sqroot/2 [when you get rid of the radical in the denominator] is once again too short of a lenght.

D. Just looking at the expression, you can see that the radical in the denominator will give you a radical in the numerator when simplified, which is actually a fraction, making the whole expression a fraction, over two. The result will be something like 5 or four point something in the middle digits.

E. Once again, the number will be too small.

This leaves you with just A.

This POE should not take long if you have done enough problems and quickly recognize patterns.

I would actually say that this is a pretty easy problem. I would say this because of the answer choices provided. All of the are pretty out there, and A is the only one that looks right. However, if there would be an answer choice of 8sqroot7 along with 9sqroot2, then it would be tougher to eliminate, and you would actually have to solve this problem.