Pythagorean Theorem
Pythagorean Theorem Word Problems
Finding Perfect Squares
Approximating Square Roots
100
What is the area of x2 (with correct units to the nearest tenth).
A) 8.6 cm2
B) 74.0 cm2
C) 9.0 cm2
D) 81.6 cm2
What is 74.0 cm2?
100
Two cars meet at an intersection. One travels north at an average speed of 80 km/h. The other travels east at an average speed of 55 km/h. How far apart are the cars after 3 h? Give your answer to one decimal place.
A) 84825.0 km
B) 300.3 km
C) 291.2 km
D) 100.5 km
What is C) 291.2 km?
100
A number that when multiplied by itself, equals that given number.
What is the square root?
100
Use prime factorization to show why 84 is not a perfect square.
What is √22 x 3 x 7 = 2√3x7 = 2√21?
200
What is BA2 equal to?
A) √ AC2 - BC2
B) BC2 - AC2
C) AC2 + BC2
D) √ BC2 - AC2
What is B) BC2 - AC2
200
A plane takes off from a local airport. It travels due north at a speed of 400 km/h. The wind blows the plane due east at a speed of 50 km/h. How far is the plane from the airport after 1 h? Give your answer to one decimal place.
A) 162500.3 km
B) 450.0 km
C) 403.1 km
D) 1350.4 km
What is C) 403.1 km?
200
Use prime factorization to find the square root of 324
What is 18?
200
Estimate the square root of 114 using perfect square benchmarks and a number line.
What is 10.6?
300
What is the length of x (to the nearest tenth)?
A) 3.3
B) 11.0
C) 4.1
D) 5.3
What is A) 3.3?
300
A 25 m ladder leans against a vertical wall. The foot of the ladder is 20 m from the base of the wall. If the foot is moved 13 m closer to the wall, how far does the top of the ladder move up the wall (to the nearest whole number)?
A) 24.0 m
B) 5.3 m
C) 3.0 m
D) 9.0 m
What is D) 9.0 km?
300
Use prime factorization to find the square root of 625.
What is 25?
300
Estimate the square root of 410 using perfect square benchmarks and a number line.
What is 20.2?
400
What is the perimeter of the trapezium, WXYZ, if WX=7m, YZ=13m, and ZW=8m to the nearest whole number?
A) 100 m
B) 128 m
C) 38 m
D) 1444 m
What is C) 38 m?
400
Find the area of a regular hexagon which has 4 cm sides (to the nearest tenth)?
A) 61.6 cm2
B) 53.7 cm2
C) 37.7 cm2
D) 41.6 cm2
What is D) 41.6 cm2
400
I am a perfect square number. The sum of my digits is 9. List 6 numbers I might be.
What is 9, 36, 81, 144, 225, 324, 441, 900, 1521, 2025, 2304, 2601, and 3600?
400
A square tabletop has an area of 30 cm2. Use an estimate (using benchmarks and a number line) what the perimeter of the tabletop is?
What is 21.6 cm.
500
The cube below has a diagonal (d) of 13.85 cm. What is its side length (to the nearest tenth)?
A) 8.0 cm
B) 11.3 cm
C) 4.3 cm
D) 7.0 cm
What is A) 8.0 cm?
500
Looking over the horizon, Geoff observes the top of a ship as it approaches directly towards him. His eye level is 5 meters above sea level and the funnel of the ship is 15 meters above sea level.
Use the two diagrams to the find the distance, x, from Geoff to the ship.
r is the radius of the Earth, equal to 6400 kilometers.
(Hint: find the distance from Geoff to the horizon and the distance of the ship to the horizon, and then add them together. Also, the second diagram is not a right triangle).
A) 25.0 km
B) 21.9 km
C) 18.3 km
D) 16.7 km
What is B) 21.9 km?
500
Use prime factorization to identify the square root of 3600
What is 60?
500
A square carpet covers 75% of the area of a floor. It's area is 119 m2. Using benchmarks and the number line, estimate the dimensions of the floor.
What is 12.6 m?