GRADED ASSESSMENT #3: Pythagorean Theorem Word Problems

Find the value if x. (Type the number only)

Answer explanation

Pythagorean Triple!

Kelly and James have a triangular shaped flower garden. The side lengths are 2 yards, 9 yards, and 11 yards. Kelly says that it is a right triangle and James says it is not a right triangle. Who is correct?

• Kelly

• James

In a park, the locations of a drinking fountain, a streetlight, and a flagpole form a right triangle. The distances are shown in the diagram. What is the missing distance from the flagpole to the streetlight (in a straight line)? Answer is rounded to the nearest whole number.

• 7 Yards

• 11 Yards

• 13 Yards

• 17 Yards

Television sizes are determined by their diagonal length. Which of the following are possible side lengths for a 65 inch TV?

• 30 in. by 35 in.

• 40 in. by 25 in.

• 45 in. by 50 in.

• 60 in. by 25 in.

Shari went to a level field to fly a kite. She let out all 85 feet of the string and tied it to a stake. Then, she walked out on the field until she was directly under the kite, which was 40 feet from the stake. How high was the kite from the ground? Type in the number only.

The main mast of a fishing boat is supported by a sturdy rope that extends from the top of the mast to the deck. If the mast is 20 feet tall and the rope attached to the deck 10 feet away from the base of the mast, how long is the rope? Round your answer to the nearest thousandth.

• 17.323 ft.

• 22.361 ft.

• 25.241 ft.

• 30.327 ft.

How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall of a house?

• 9 ft.

• 14 ft.

• 19 ft.

• 20 ft.

Two cyclist start from the same location. One cyclist travels due north for 6 miles and the other due east for 8 miles. What is the shortest distance between the two cyclists? Type in the number only.

The base of a 25-foot ladder is positioned 10 feet from the bottom of the building it leans against. An extension can be pulled out to make it a 30-foot ladder.

Part A: Without the extension, can the ladder reach a window that is 24 feet above the ground? Justify your reasoning with mathematics.

• Yes, because the ladder will reach greater than 24 feet.

• Yes, because the ladder will reach exactly 24 feet.

• No, because the ladder will reach less than 24 feet.

Part B: With the extension, can the ladder reach a window that is 28 feet above the ground? Justify your reasoning with mathematics. (Remember an extension can be pulled out to make it a 30 foot ladder)

• Yes because the ladder will reach greater than 28 feet.

• Yes, because the ladder will reach exactly 28 feet.

• No, because the ladder will reach less than 28 feet.