In the figure shown below, ABCD is a rectangle, EFGH is a square

In the figure shown below, ABCD is a rectangle, EFGH is a square, and CD is the diameter of a semicircle. Point K is the midpoint of CD. Point J is the midpoint of both AB and
EF. Points E and F lie on AB. The 3 given lengths are in meters.

1. The length of EH is what percent of the length of AD?

  1. 15.6%
  2. 30%
  3. 36%
  4. 43.2%
  5. 50%

2. What is the length, in meters, of JD?

  1. 13
  2. 15.6
  3. 17
  4. √44
  5. √244

3. What is the length, in meters, of arc CD ?

  1. 2.5π
  2. 6.25π
  3. 10π
  4. 25π

4. The figure will be placed in the standard (x,y) coordinate plane so that K is at the origin, AB is parallel to the x-axis, and 1 meter equals 1 coordinate unit. Which of the following values could be the y-coordinate of H ?

  1. 1.8
  2. 3.6
  3. 8.4
  4. 10
  5. 12

Answers

1. The correct answer is B.

EFGH is a square so HG = EF = 3.6 meters, and ABCD is a rectangle with AD and BC as opposing sides so AD = BC = 12 meters. The ratio of the length of EH to the length of AD is 3.6/12 = 0.3, so the length of EH is 0.3 x (100)% = 30% percent of the length of AD.

2. The correct answer is A.

You can form a right triangle using AD and AJ as the legs and JD as the hypotenuse. The length of AD is 12 meters, and the length of AJ is 10/2 = 5 meters. By the Pythagorean theorem, JD = √(122 + 52) = 13 meters.

3. The correct answer is B.

Using the fact that the circumference of a circle is π times the diameter of the circle, you can compute the length of arc CD by finding 1/2 of the circumference of the circle centered at K with radius CK = 10/2 = 5 meters. So, 1/2 x (10π) = 5π meters.

4. The correct answer is C.

The y-coordinate of E is 12 because E lies on AB , and AB lies on the line y = 12. Segment EH is perpendicular to AB and has length 3.6 coordinate units. Therefore, H has y-coordinate 12 - 3.6 = 8.4.