Below are the 2017 Grade 9 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the **Past Tests** and **All Posts** pages.

26.) Find all possible values of *x* in the proportion (*x* – 3) : (*x* – 1) = (*x* + 6) : 20.

27.) An angle in a quadrilateral has measures , while the others have degree measures in the ration 3 : 5 : 7. Find the measure of the largest angle.

28.) In rhombus . Find

29.) The diagonals of rhombus *STAY* intersect at *X*. If and find the length (in units) of the shorter diagonal.

30.) Find the perimeter (in units) of the rhombus *STAY* in the previous problem.

31.) In parallelogram , and . Find *x*.

32.) In parallelogram Find *x*.

33.) (Figure 1) In parallelogram and *E* is chosen on diagonal *BD* so that *DE = DC*. Find

34.) In an iscosceles trapezoid, the lengths (in units) of the diagonals are 3*x* + 2 and 5*x* – 8. Find *x*.

35.) In trapezoid where and If *R* and *S* are the midpoints of *MQ* and *NP*, respectively, find the length (in units) of *RS*.

36.) The diagonals of quadrilateral *POST* are perpendicular, and intersect at *E*. Suppose that , *SE* is twice as long as *PE*, and the area of the quadrilateral is 18 sq.units. Find the length (in units) of SE.

37.) Suppose $latex *ST* = 2, *QR* = 6, $ and $latex *PT* = 5. $ Find *PR*.

38.) Suppose $latex* ST* = 4, *QR* = 5, $ and the perimeter of is 14. Find the perimeter (in units) of

39.) Suppose , and Find *x*.

40.) The sides of are 9 cm, 10 cm, and 12 cm. If find the length of the longest side of if its shortest side is 6 cm.

41.) Two similar triangles have lengths of corresponding sides in the ratio 4 : 5. Find the ratio of their areas.

42.) Given the points of and on the plane, the point *E* is chosen in the first quadrant such that and . Find the coordinates of *E*.

43.) (Figure 2) In the figure, and If and which triangle (whose sides already drawn) is similar to

For problems 44 – 46

In Let E be the point on *AC* so that

44.) Suppose *AE* = 9 and *CE* = 2. Find *BE* (in units).

45.) Suppose *AE* = 30 and *CE* = 6. Find *BC* (in units).

46.) Suppose *AB* = 12 and Find* CE*.

47.) Two sides of a rectangle are 9 cm and 12 cm long. Find the length of a diagonal.

48.) A ladder is leaning against a vertical wall with the top 5 m above the ground. The top of the ladder slides all the way down the wall so that the bottom of the ladder slides 1 meter away fromthe wall. How long is the ladder?

49.) The two legs of a right triangle are in the ratio If the hypotenuse is 9 units long, find the area (in square units) of the triangle.

50.) In and Find cos *B*.

Answer key:

26.) x = 6, 9

27.)

28.)

29.) 10

30.) 52

31.) 3

32.) 20

33.)

34.) 5

35.) 6.5

36.) 4

37.) 15

38.) 17.5 or

39.) 9

40.) 8 cm

41.) 16 : 25 or

42.) (13, 3)

43.)

44.)

45.)

46.)

47.) 15 cm

48.) 13 m

49.)

50.) or 0.8

View Part I here: 2017 Grade 9 Math Challenge – Elimination Round with answer key – Part I