MathDB

4

Part of 2005 AMC 10

Problems(2)

Rectangle Area

Source:

1/14/2009
A rectangle with a diagonal of length x x is twice as long as it is wide. What is the area of the rectangle? <spanclass=′latex−bold′>(A)</span> 14x2<spanclass=′latex−bold′>(B)</span> 25x2<spanclass=′latex−bold′>(C)</span> 12x2<spanclass=′latex−bold′>(D)</span> x2<spanclass=′latex−bold′>(E)</span> 32x2 <span class='latex-bold'>(A)</span>\ \frac14x^2 \qquad <span class='latex-bold'>(B)</span>\ \frac25x^2 \qquad <span class='latex-bold'>(C)</span>\ \frac12x^2 \qquad <span class='latex-bold'>(D)</span>\ x^2 \qquad <span class='latex-bold'>(E)</span>\ \frac32x^2
geometryrectangle
Diamond Operation

Source:

1/14/2009
For real numbers a a and b b, define a \diamond b \equal{} \sqrt{a^2 \plus{} b^2}. What is the value of (5\diamond 12)\diamond ((\minus{}12) \diamond (\minus{}5))? <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 172<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 132<spanclass=′latex−bold′>(E)</span> 26 <span class='latex-bold'>(A)</span>\ 0\qquad <span class='latex-bold'>(B)</span>\ \frac{17}{2}\qquad <span class='latex-bold'>(C)</span>\ 13\qquad <span class='latex-bold'>(D)</span>\ 13\sqrt{2}\qquad <span class='latex-bold'>(E)</span>\ 26