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