Grade 7 Geometry: Pythagorean Theorem & Scale Models

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. How long is the ladder?

• 10 feet

• 8 feet

• 12 feet

• 14 feet

A rectangular garden measures 10 meters in length and 6 meters in width. If you want to create a path that is 1 meter wide around the garden, what will be the area of the path?

• 20 square meters

• 24 square meters

• 30 square meters

• 36 square meters

A right triangle has one leg that measures 5 cm and another leg that measures 12 cm. What is the length of the hypotenuse?

• 15 cm

• 10 cm

• 14 cm

• 13 cm

A scale model of a house is built at a scale of 1:50. If the actual house is 10 meters wide, how wide is the model?

• 0.5 meters

• 2 meters

• 1 meter

• 0.2 meters

A square park has a side length of 20 meters. If a walking path that is 2 meters wide is built around the park, what will be the total area of the park including the path?

• 484 square meters

• 400 square meters

• 256 square meters

• 576 square meters

A right triangle has a base of 9 inches and a height of 12 inches. What is the length of the hypotenuse using the Pythagorean theorem?

• 13 inches

• 10 inches

• 18 inches

• 15 inches

A rectangular swimming pool is 15 meters long and 10 meters wide. If you want to increase the dimensions of the pool by a scale factor of 2, what will be the new dimensions?

• 30 meters long and 20 meters wide

• 30 meters long and 25 meters wide

• 20 meters long and 10 meters wide

• 25 meters long and 15 meters wide

A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? Use the Pythagorean theorem to justify your answer.

• No, this triangle cannot exist.

• No, this triangle is an obtuse triangle.

• Yes, this triangle is an equilateral triangle.

• Yes, this triangle is a right triangle.

A rectangular field is 50 meters long and 30 meters wide. If a fence is built around the field, what is the total length of the fence?

• 160 meters

• 140 meters

• 180 meters

• 120 meters

A model of a car is built at a scale of 1:25. If the actual car is 4 meters long, how long is the model?

• 0.25 meters

• 0.2 meters

• 0.16 meters

• 0.1 meters