Exploring Pythagorean Theorem & Graphing Linear Equations

A ladder is leaning against a wall. The foot of the ladder is 4 feet away from the wall, and the ladder reaches a height of 3 feet on the wall. Use the Pythagorean theorem to find the length of the ladder. Then, write the linear equation representing the relationship between the height of the ladder and the distance from the wall.

• The length of the ladder is 5 feet and the linear equation is h = sqrt(25 - d^2).

• The length of the ladder is 6 feet and the linear equation is h = 6 - d.

• The length of the ladder is 7 feet and the linear equation is h = d^2 - 4.

• The length of the ladder is 4 feet and the linear equation is h = 4 + d.

A right triangle has one leg measuring 5 cm and the other leg measuring x cm. If the hypotenuse is 13 cm, use the Pythagorean theorem to find the value of x. Then, express the relationship between the legs and the hypotenuse as a linear equation and graph it.

• 10 cm

• 8 cm

• 12 cm

• 15 cm

A baseball diamond is a square with each side measuring 90 feet. If you want to find the distance from home plate to second base, use the Pythagorean theorem. After finding the distance, write a linear equation that represents the relationship between the distance and the side length of the diamond.

• d = s + 90

• d = s/2

• d = s√2

• d = s^2

A ramp is built to help wheelchair access to a building. The ramp is 12 feet long and rises to a height of 5 feet. Use the Pythagorean theorem to find the horizontal distance from the base of the ramp to the building. Then, graph the linear equation that represents the height of the ramp as a function of the horizontal distance.

• The horizontal distance is 8 feet.

• The horizontal distance is 12 feet.

• The horizontal distance is 15 feet.

• The horizontal distance from the base of the ramp to the building is approximately 10.91 feet.

A right triangle has legs measuring 8 inches and 15 inches. Use the Pythagorean theorem to find the length of the hypotenuse. Then, create a linear equation that relates the lengths of the legs to the hypotenuse and graph it.

• The length of the hypotenuse is 17 inches.

• The length of the hypotenuse is 20 inches.

• The length of the hypotenuse is 10 inches.

• The length of the hypotenuse is 12 inches.

A swimming pool is rectangular, measuring 20 meters by 15 meters. If you want to install a diagonal support beam, use the Pythagorean theorem to find the length of the beam. Then, write a linear equation that represents the relationship between the length and width of the pool and graph it.

• The length of the diagonal support beam is 25 meters.

• 15 meters

• 30 meters

• 20 meters

A kite is flying at a height of 30 meters, and the string makes a 60-degree angle with the ground. Use the Pythagorean theorem to find the length of the string. Then, express the relationship between the height and the length of the string as a linear equation and graph it.

• 15 meters

• 25√2 meters

• 40 meters

• 20√3 meters

A triangular park has a base of 24 meters and a height of 10 meters. Use the Pythagorean theorem to find the length of the hypotenuse if the park is shaped like a right triangle. Then, create a linear equation that relates the base and height to the hypotenuse and graph it.

• 26 meters

• 22 meters

• 20 meters

• 30 meters