Math problem in the Blue Book is killing me

<p>It's on page 852, question #20. It's hard to explain without the picture, but basically you have a quarter circle with a rectangle flush with the corner and center of the circle. They want the perimeter of the outside arc, and the inside part, except for a diagonal going through the rectangle.</p>

<p>It's easy to figure out that the outside arc is 3pi, and that the diagonal of the rectangle is 6, since the other diagonal of the rectangle is a radius (and the problem said the radius was 6). So we're left with a right triangle with a hypotenuse of 6. So far, so good, but we need to find the lengths of the sides of the rectangle to finish.</p>

<p>The problem tells us that the sides add up to 8, but they can't be integers, since the hypotenuse is 6. Interestingly, when I tried picking the values of 5 and 3, I get the correct answer of 10 + 3pi. But there's no way to have a right triangle with sides of 3,5, and 6.</p>

<p>I tried playing around with x+y=8 and x2 + y2 = 36 and subsitituing, but that only got me to x2 - 8x + 14, which doesn't seem FOILable.</p>

<p>Anyone know how to solve this? I really appreciate the help.</p>

<p>Well you know RS and RT are 6(both radius), so you subtract 8 from 12 and get 4. Add that to the 3pi and you get your answer.</p>

<p>Thanks so much! I was so focused on finding the values for each side that I forgot you don’t really need to know that to answer the problem.</p>

<p>lol had trouble on the same one but BB online answers helped me</p>