Pythagorean Theorem: Algebra and Geometry in Action

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a height of 8 feet on the wall. Use the Pythagorean theorem to find the length of the ladder.

• 10 feet

• 14 feet

• 12 feet

• 8 feet

A rectangular garden has a length of 10 meters and a width of 6 meters. If you want to plant a diagonal path from one corner to the opposite corner, how long will the path be?

• 10.50 meters

• 9.00 meters

• 12.00 meters

• 11.66 meters

A right triangle has one leg measuring 9 cm and the other leg measuring x cm. If the hypotenuse is 15 cm, find the value of x using the Pythagorean theorem.

• 16 cm

• 10 cm

• 14 cm

• 12 cm

A 12-foot tall tree casts a shadow that is 9 feet long. If you were to walk directly from the top of the tree to the end of the shadow, how far would you walk? Use the Pythagorean theorem to find the distance.

• 18 feet

• 9 feet

• 12 feet

• 15 feet

A triangular park has one side measuring 5 meters and another side measuring 12 meters. If the park is a right triangle, what is the length of the third side?

• 7 meters

• 9 meters

• 15 meters

• 10.91 meters

A right triangle has legs of lengths 7 cm and x cm. If the hypotenuse is 10 cm, find the value of x using the Pythagorean theorem.

• 5 cm

• 8 cm

• 12 cm

• √51 or approximately 7.14 cm

A kite is flying at a height of 30 meters. If the string of the kite is 50 meters long, how far is the kite from the point on the ground directly below it?

• 20 meters

• 60 meters

• 30 meters

• 40 meters

A square has a diagonal that measures 14 cm. What is the length of one side of the square? Use the Pythagorean theorem to find your answer.

• 10 cm

• 14 cm

• 7√2 cm

• 5√2 cm

A right triangle has one leg measuring 8 inches and a hypotenuse measuring 10 inches. What is the length of the other leg?

• 7 inches

• 5 inches

• 6 inches

• 9 inches

A rectangular swimming pool is 15 meters long and 20 meters wide. If you want to swim diagonally from one corner to the opposite corner, how far will you swim?

• 15 meters

• 25 meters

• 20 meters

• 30 meters