This is the 2018 Grade 9 Math Challenge Elimination Level Questions – Part 2 with answers. Questions in the previous years can be accessed on the **Past Tests** page and all questions can be found in the** All Posts** page.

26.) Find all possible values of *n* in the proportion (*n* – 5) : (*n* – 3) = (*n* + 3) : 20.

27.) An angle in a quadrilateral has measures 45°, while the others have degree measures in the ratio 5 : 7 : 9. Find the measure of the largest angle.

28.) In rhombus *QRTS*, Find angle *RTS*.

29.) The diagonals of the rhombus *PRAY* intersect at *G*. If *AG* = 3*n*, *PG* = 6, *RG* = 3*m* – 2*n*, and *YG* = *m* + 2*n*, find the length (in units) of the shorter diagonal.

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

31.) In parallelogram *ABCD*, *AB* = 8, *BC* = 5, *CD* = 7*x* – 2*y*, and *AD* = *z* + *y*. Find *x*.

32.) In parallelogram *LMNO*, Find *x*.

33.) In an isosceles trapezoid, the lengths of the diagonals are 2*x* + 3 and 6*x* – 5. Find *x*.

34.) The diagonals of quadrilateral *ABCD *are perpendicular and they intersect at *E*. If *BE* = *DE* = 4, *AC* is twice as long as *EC*, and the area of the quadrilateral is 24 sq. units. Find the length (in units) of *AE*.

35.) The sides of are 5 cm, 7 cm and 10 cm. If find the length of the shortest side of if its longest side is 15 cm.

36.) The ratio of the lengths of corresponding sides of two similar triangles is 3 : 4. Find the ratio of their areas.

37.) Given the points *P*(0, 0), *Q*(12, 0), *R*(24, 0) and *S*(6, 6) on the plane, the point *T* is chosen so that *PS* || *QT* and *QS* || *RT*. Find the coordinates of *T*.

38.) Two sides of a rectangular are 10 cm and 24 cm. Find the length of a diagonal.

39.) The two legs of a right triangle are in the ratio If the hypotenuse is 10 units long, find the area (in square units) of the triangle.

40.) In and sin A = Find sin *B*.

(For problems 41 – 43. )In Let *D* be a point on *AB *so that

41.) Suppose *AD* = 9 and *BD *= 4. Find *CD *in units.

42.) Suppose *AD *= 20 and *BD *= 5. Find *BC *in units.

43.) Suppose *AC *= 24 and Find *BC* in units.

44.) A ladder is leaning against a vertical wall which is 5m high. The top of the ladder slides all the way down the wall so that the bottom of the ladder slides 1m away from its original position. How long is the ladder?

Answer key:

26.) *n* = 7, 13

27.) 135°

28.) 15°

29.) 12

30.) 40

31.) *x* = 2

32.) *x* = 25°

33.) *x* = 2

34.) 3/2 units

35.) *x* = 7.5 cm

36.) 9 : 16

37.) (18, 6)

38.) 26

39.)

40.) 12/13

41.) 6

42.)

43.) 13m

View Part 1 here:2018 Grade 9 Math Challenge Elimination Level Questions – Part 1