MathDB

6

Part of 2019 MIG

Problems(2)

2019 Individual #6

Source:

5/1/2022
How many rectangles are in the following figure? [asy] size(80); draw((0,0)--(3,0)--(3,4)--(0,4)--cycle); draw((0,2)--(3,2)); draw((0.75,2)--(0.75,0)); draw((2.25,2)--(2.25,0)); [/asy] <spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>9<span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>9
2019 Individual
2019 Team #6

Source:

5/1/2022
Square ABCDABCD has side length 44. Side ABAB is extended to point EE so that AEAE has the same length as ACAC, as shown below. What is the length of ECEC? Express your answer as a decimal to the nearest hundredth. [asy] size(80); defaultpen(fontsize(8pt)); pair EE = (4sqrt(2),0); pair A = (0,0); pair B = (4,0); pair C = (4,4); pair D = (0,4); draw(A--B--C--D--cycle); draw(A--EE); draw(C--EE,dotted); label("AA",A,SW); label("BB",B,S); label("CC",C,N); label("DD",D,N); label("EE",EE,S); [/asy]
2019 Team