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Please solve all the math problems in the Pdf showing all your workings no long explanations required.

Applications of Quadratics, Pythagorean Theorem and Distance Formula Problem Set

Problems #1-10: Two sides of triangle ABC are given. Find the length of the missing side. Leave your answer in exact form, and

then round answers to 2 decimal places if needed.

A

1.

2.

3.

4.

5.

a 6 ft and b 8 ft

a 12 in and c 15 in

a 2 ft and b 5 ft

b 6 ft and c 9 ft

a 14 cm and b 3 cm

6.

7.

8.

9.

10.

a 8 m and c 10 m

a 17 yd and b 13 yd

a 1 mi and c 4 mi

a 7 in and b 11 in

a 3 ft and b 3 ft

c

B

b

a

C

Problems #11-15: Solve the following application problems using the Pythagorean Theorem. Leave your answer in exact form, and

then round answers to 2 decimal places if needed.

11. Maria walked 3 km west and then 4 km south. How far is Maria from her starting point?

12. David leaves the house to go to school. He walks 200 m west and 125 m north. How far away is the school from his house?

13. Laptop screen sizes are determined by the length of the diagonal portion of the screen, rounded to the nearest whole number. A

laptop screen has a 10 inch width and the height measures 8 inches. What is the screen size of the laptop?

14. A 10 foot ladder is placed 5 ft from the bottom of the wall. How far up the wall does the ladder reach?

15. A 13 foot ladder is used to reach a window that is 12 feet above ground. How far from the base of the building is the ladder?

Problems #16-20: Find the exact distance between each pair of points.

16.

19.

5, 2 and 4,14

1, 6 and 3, 4

17.

20.

88, 20 and 80, 24

4,7 and 4, 5

18.

10, 4 and 2, 2

Problems #21-25: Use the steps to problem solving to translate the following applications to quadratic equations to solve.

21. A rectangular hall rug covers an area of 63 ft2. Find the dimensions of the rug if it is seven times longer than it is wide.

22. Pool tables are rectangular, and their length is twice the width. Find the dimensions of a pool table if it covers 50 ft 2 of floor

space.

23. A rectangular shaped x-ray film has an area of 80 square inches. The length is 2 inches longer than the width. Find its width and

length.

24. A triangular sail has a height that is three times longer than the width of its base. If the sail has an area of 24 ft 2, find the height

and the length of the base.

25. The length of the base of a triangular sheet of canvas above the door of a tent is 2 feet more than twice its height. The area is 30

square feet. Find the height and the length of the base of the triangle.

Problems #26-28: Quadratic Equation Model Problems

26. A pitcher can throw a fast ball at 79 feet per second. If he throws the ball into the air with that velocity, its height h in feet, t

seconds after being released, is approximated by h 16t 2 79t 5 . After the ball is thrown, in how many seconds will it hit the

ground?

27. A pitcher can throw a fast ball underhand at 63 feet per second (about 45 miles per hour). If she throws a ball into the air with

that velocity, its height h in feet, t seconds after being released, is approximated by h 16t 2 63t 4 . After the ball is thrown, in

how many seconds will it hit the ground?

28. The height h in feet reached by a dolphin t seconds after breaking the surface of the water is given by h 16t 2 32t . How long

is the dolphin out of water when it jumps?

Answers:

1. 10 ft

2. 9 in

3. 29 5.39 ft

4. 3 5 6.71 ft

5. 205 14.32 cm

6. 6 m

7.

458 21.40 yd

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

15 3.87 mi

170 13.04 in

3 2 4.24 ft

5 km

25 89 235.85 m

13 in

5 3 8.66 ft

5 ft

15

4 5

10

2 5

4 13

3 ft, 21 ft

5 ft, 10 ft

8 in, 10 in

12 ft, 4 ft

5 ft, 12 ft

5 sec

4 sec

2 sec

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