Question

1. ABCD is a rectangle. BD is a straight line that cuts the rectangle into equal halves. The ratio of the area of P to the area of Q is 2 : 5, and the ratio of the area R to the area of S is 4 : 3. The area of S is 9 square centimeters.
  a)   Find the ratio of the area of R to the area of the rectangle.   Find the area of the rectangle

Answer 1

S is 3 parts of R, or 9.  9 is 3/4 of 12, so R is 12. 12 plus 9 is 21, which is half of the full area of the rectangle. The area of the rectangle is 42 square centimeters. Now, we need to find what R is to the whole rectangle. We know that R is 12 square centimeters, and that the rectangle is 42 square centimeters. That ratio is 12 to 42. If it is simplified, that would be 6 to 21. If it is simplified further, you find that it is 2 to 7. Hope this wasn't too confusing, and I hope that I helped :)