Pythagorean Theorem (8.G.7 & 8.G.8)

Determine whether the lengths listed form a right triangle: 8, √23, √87

It is a right triangle, because 64+23 = 87.

Determine whether the lengths listed form a right triangle: 4, 11, √103

It is not a right triangle, because 16+103≠121. This triangle is obtuse.

Find the distance between the points with the given coordinates: (10, 3) and (-4, 9). Round to the nearest tenth, if necessary.

15.2 units

The diagonal of a rectangle is 25 cm. The width is 15 cm. What is the length?

20 cm.

A right triangle has a leg that measures 10 m. Its hypotenuse is 26 m. What is the length of the missing leg?

24 cm

A rectangle measures 24 in by 7 in. What is the length of its diagonal?

25 in.

A 35 foot ladder is leaned against a wall. If the base of the ladder is 12 feet from the wall, how many feet high will the ladder reach?

32.9 ft

Peter regularly takes a short-cut across Mr. Henry's lawn instead of walking on the sidewalk (8 m by 15 m) on his way home from school. How many meters is saved by Joe cutting diagonally across the lawn?

6 meters

The length of a rectangle is 8 cm. Its diagonal measures 14 cm. What is its width?

about 11.5 cm.

A baseball diamond is a square with sides of 80 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?

about 113.1 ft.

Two snails being at the same place in the garden. One snail travels six cm north. Another travels fourteen cm west. How far apart will they be?

about 15.2 cm.

An 18 ft string is tied to the top of a pole and pulled to the ground 7ft away from the pole. How tall is the pole?

about 16.6 ft.