Indirect Measurement: Area and Pythagorean Problems

A tree casts a shadow of 15 feet. If a 5-foot tall person stands next to the tree and casts a shadow of 3 feet, how tall is the tree using indirect measurement?

• 10 feet

• 20 feet

• 30 feet

• 25 feet

A ladder leans against a wall, reaching a height of 12 feet. If the base of the ladder is 5 feet away from the wall, how long is the ladder?

• 13 feet

• 10 feet

• 15 feet

• 8 feet

A rectangular garden has a length of 10 meters and a width of 6 meters. If a path of 1 meter wide is built around the garden, what is the area of the path?

• 12 square meters

• 24 square meters

• 48 square meters

• 36 square meters

A kite is flying at a height of 30 feet. If the string is 50 feet long, how far is the kite from the person holding the string?

• 20 feet

• 30 feet

• 60 feet

• 40 feet

A right triangle has one leg measuring 8 cm and the other leg measuring 6 cm. What is the length of the hypotenuse?

• 12 cm

• 14 cm

• 10 cm

• 8 cm

A rectangular swimming pool is 20 meters long and 10 meters wide. If a deck surrounds the pool that is 2 meters wide, what is the area of the deck?

• 120 square meters

• 136 square meters

• 100 square meters

• 150 square meters

A flagpole casts a shadow of 10 feet. If a 2-foot tall person casts a shadow of 4 feet, how tall is the flagpole?

• 5 feet

• 3 feet

• 8 feet

• 12 feet

A right triangle has a hypotenuse of 13 cm and one leg measuring 5 cm. What is the length of the other leg?

• 6 cm

• 8 cm

• 12 cm

• 10 cm

A rectangular field measures 50 meters by 30 meters. If a path of 2 meters wide is built around the field, what is the area of the path?

• 180 square meters

• 250 square meters

• 400 square meters

• 336 square meters

A person stands 10 feet away from a building and sees the top of the building at an angle of elevation of 30 degrees. How tall is the building?

• 8.66 feet

• 10 feet

• 3.46 feet

• 5.77 feet