Pythagorean Theorem Questions
(1) Hawick is 15 miles south of Abbotsford, and Kelso is 17 miles east of Abbotsford. What is the
distance from Hawick to Kelso? Round your answer to the nearest tenth of a mile.
(2) A flagpole broke in a storm. It was originally 81 feet tall. 28 feet are still sticking straight out of
the ground, where it snapped, but the remaining piece has hinged over and touches the ground
some distance away. What is the distance between the two points where the flagpole touches
the ground?
(3) A football field is a 64-meter-wide, 100-meter-long rectangle. What is the length of a diagonal of
a football field to the nearest meter?
(4) Ryan is putting a clothesline in his rectangular backyard. He wants to put it between two trees
on the edge of his property. He has measured his property, and made the sketch shown below,
where all the lengths listed are in meters. What is the smallest length of rope that Ryan could
buy which would stretch from one tree to the other?
(5) Steve is turning half of his backyard into a chicken pen. His backyard is a 24-meter by 45-meter
rectangle. He wants to put a chicken wire fence along the west side of the yard, the south side
of the yard, and along the diagonal connecting the northwest to the southeast corner of the
yard. How many meters of fencing will Steve need to fully enclose this area?
(6) Julian jogs 2 kilometers east, 4 kilometers north, and then 7 kilometers west. How far is Julian
from his starting position, to the nearest tenth of a kilometer?
(7) Pipestone, Marshall, and Worthington are three cities. Pipestone is 36 miles west of Marshall,
and Worthington is 77 miles north of Marshall. Bert and Tre leave Pipestone at the same time.
Bert goes straight to Worthington at a speed of 25 miles per hour. Tre goes from Pipestone to
Marshall to Worthington at a speed of 35 miles per hour. Who will get to Worthington first?
How much longer will it take for the second person to arrive? Round to the nearest tenth of an
hour.
(8) What is the area of the triangle shown below?
(9) The ancient Egyptians had a neat way to construct right angles. They would make a long rope
with knots in it. When they bent the rope into a triangle, they always got a right angle. This was
useful when planning the pyramids, for example. Which of the sets of three numbers listed
would let you form a right angle in this way? Select all that apply.
a. {6, 11, 8}
b. {16, 63, 65}
c. {1, 1, 1}
d. {51, 149, 140}
e. {13, 30, 24}
(10)Omar is fixing his garage, which looks like it has started to lean over. He is not sure if it is straight
or slanted slightly like shown below. He has measured that the distance along the floor from one
corner to the other is 20 meters, and the distance from the bottom left to top left corner is 21
meters. To add another check, he measures the distance from the top left to the bottom right
corner: it is 29 meters. Is Omar's garage straight? If not, how long should the diagonal be to
make it straight?