Acute, right or obtuse from the sides, Pythagorean triples, and 45-45-90 and 30-60-90 triangles

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Kira has two sticks, 5 cm and 12 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?

   6 lengths
2. 2.

   Luz has two sticks, 8 cm and 15 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?

   10 lengths
3. 3.

   Milo has two sticks, 12 cm and 16 cm long. A third stick is a whole number of centimeters and must close a real triangle. How many lengths make an obtuse triangle?

   13 lengths

4. Read this first

   Use this

   Not to scale.

5. 4.

   Pia's map tile is a regular hexagon with 4-cm sides. What is its area in square centimeters, in simplest radical form?

   24√3
6. 5.

   Ren's tent floor is a regular hexagon with 6-cm sides. What is its area in square centimeters, in simplest radical form?

   54√3
7. 6.

   Tala's quilt patch is a regular hexagon with 8-cm sides. What is its area in square centimeters, in simplest radical form?

   96√3
8. 7.

   Regular hexagon with 10-cm sides. Not to scale. Zee's table top is a regular hexagon with 10-cm sides. What is its area in square centimeters, in simplest radical form?

   150√3

9. Use this

   Not to scale.

10. 8.

    Ari packs a straight rod in a box 2 in by 3 in by 6 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?

    7 inches
11. 9.

    Esme packs a straight rod in a box 3 in by 4 in by 12 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?

    13 inches
12. 10.

    Jun packs a straight rod in a box 9 in by 12 in by 20 in. How long, in inches, is the longest rod that fits from one corner to the opposite corner?

    25 inches