Pythagorean Theorem: Algebra and Graphical Challenges

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. Write an algebraic expression for the length of the ladder.

• 14 feet

• 8 feet

• 10 feet

• 12 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? Use the Pythagorean theorem and express your answer algebraically.

• 8√2 meters

• 5√10 meters

• 2√34 meters

• 12 meters

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

• 10

• 14

• 16

• 12

A baseball diamond is a square with each side measuring 90 feet. What is the distance from home plate to second base? Use the Pythagorean theorem to find the answer and represent it graphically.

• 45√2 feet (approximately 63.64 feet)

• 90√2 feet (approximately 127.28 feet)

• 180 feet

• 90 feet

A 12-foot tall tree casts a shadow of 9 feet. If you were to draw a right triangle with the tree and its shadow, what is the distance from the top of the tree to the end of the shadow? Use the Pythagorean theorem to find the distance and express it algebraically.

• 10 feet

• 15 feet

• 12 feet

• 18 feet

A triangular park has sides measuring 7 meters, 24 meters, and 25 meters. Determine if this triangle is a right triangle using the Pythagorean theorem. Show your work with an algebraic expression.

• No, it is an obtuse triangle.

• Yes, it is a right triangle.

• Yes, it is an equilateral triangle.

• No, it is a scalene triangle.

You are designing a triangular kite with a base of 10 inches and a height of 24 inches. What is the length of the diagonal string that connects the top of the kite to the bottom corner? Use the Pythagorean theorem to find the length and represent it graphically.

• 20 inches

• 24.5 inches

• 15 inches

• 30 inches

A right triangle has legs measuring 5x and 12x. If the hypotenuse is 13x, write an equation using the Pythagorean theorem and solve for x. What are the lengths of the legs?

• The lengths of the legs are 5 and 12.

• The lengths of the legs are 10 and 14.

• The lengths of the legs are 3 and 4.

• The lengths of the legs are 6 and 8.

A swimming pool is rectangular, measuring 15 meters by 20 meters. If you want to swim diagonally from one corner to the opposite corner, how far will you swim? Use the Pythagorean theorem to calculate the distance and express it algebraically.

• 25 meters

• 15 meters

• 20 meters

• 30 meters

A construction worker needs to place a support beam diagonally across a rectangular frame that is 4 feet wide and 3 feet tall. What is the length of the beam? Use the Pythagorean theorem to find the length and represent it graphically.

• 6 feet

• 5 feet

• 4 feet

• 7 feet