Right Triangles: Ratios & Pythagorean Theorem Challenge

A ladder leans against a wall, forming a right triangle. If the ladder is 10 feet long and reaches a height of 8 feet on the wall, how far is the base of the ladder from the wall? Use the Pythagorean theorem to find the distance.

• 10 feet

• 8 feet

• 4 feet

• 6 feet

Two similar right triangles have side lengths in the ratio of 3:4. If the shorter side of the smaller triangle is 6 cm, what is the length of the shorter side of the larger triangle?

• 10 cm

• 6 cm

• 8 cm

• 12 cm

A 5-foot tall person casts a shadow of 3 feet. At the same time, a tree casts a shadow of 12 feet. How tall is the tree? Use the concept of similar triangles to solve.

• 10 feet

• 25 feet

• 15 feet

• 20 feet

In a right triangle, one leg measures 9 cm and the other leg measures 12 cm. What is the length of the hypotenuse? Apply the Pythagorean theorem to find the answer.

• 10 cm

• 13 cm

• 17 cm

• 15 cm

A model of a building is made using similar triangles. If the height of the model is 2 meters and the actual building is 10 meters tall, what is the ratio of the height of the model to the height of the building?

• 1/5

• 2/5

• 1/3

• 1/4

A right triangle has one angle measuring 30 degrees. If the length of the hypotenuse is 20 cm, what is the length of the side opposite the 30-degree angle? Use the properties of similar triangles to find the answer.

• 25 cm

• 5 cm

• 15 cm

• 10 cm

Two similar right triangles have corresponding side lengths of 5 cm and 15 cm. If the longer side of the smaller triangle is 12 cm, what is the length of the longer side of the larger triangle?

• 30 cm

• 24 cm

• 36 cm

• 18 cm

A flagpole casts a shadow of 15 feet. At the same time, a 6-foot tall person casts a shadow of 3 feet. How tall is the flagpole? Use the concept of similar triangles to solve this problem.

• 20 feet

• 25 feet

• 30 feet

• 35 feet

In a right triangle, the lengths of the legs are in the ratio of 5:12. If the longer leg measures 24 cm, what is the length of the shorter leg? Use ratios to find the answer.

• 20 cm

• 15 cm

• 12 cm

• 10 cm

A right triangle has legs measuring 8 cm and 15 cm. What is the area of the triangle? Use the formula for the area of a triangle and apply the Pythagorean theorem to find the hypotenuse if needed.

• 120 cm²

• 60 cm²

• 75 cm²

• 45 cm²