# Question 1 A triangle has squares on its three sides as shown below. What is the value of x? Three squares having side lengths 9 cm, x cm, and 12 cm joining to form right triangle at the center 12 inches 15 inches 108 inches 144 inches Question 2 Mona filled the glasses shown below completely with water. The total amount of water that Mona poured into the glasses is 100 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale. A cylinder with width 5 and height unknown is labeled glass 1, and a cone with height 5.2 and width 6 is labeled glass 2. 2.6 centimeters 4.8 centimeters 5.6 centimeters 7.4 centimeters Question 3 The length of the hypotenuse of a right triangle is 137 units. The length of one leg of the triangle is 105. Gina wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1372 − 1052 = 18,769 − 11,025 = 7,744 units Which statement best explains whether Gina's step is correct or incorrect? It is incorrect because the length of the unknown side is the square root of 29,794. It is incorrect because the length of the unknown side is the square root of 7,744. It is correct because the length of the unknown side is the difference of the lengths of the sides. It is correct because the length of the unknown side is the difference of the squares of the sides. Question 4 What is the volume of a sphere with a radius of 3 inches? 12π cubic inches 24π cubic inches 36π cubic inches 48π cubic inches Question 5 A right triangle PQR is shown with the right angle at Q. The length of side PQ is labeled as 36 cm, and the length of side QR is labeled as 48 cm. What is the length (in centimeters) of side PR of the triangle? 36 centimeters 42 centimeters 60 centimeters 84 centimeters Question 6 ABCD is a rectangle. What is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53 feet 28 feet 45 feet 53 feet 98 feet Question 7 Look at the cups shown below (images are not drawn to scale): A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. 18.8 cubic inches 21.2 cubic inches 28.2 cubic inches 49.5 cubic inches Question 8 What is the length of leg y of the right triangle? A right triangle with hypotenuse 26 and legs 24 and y 10 14 24 26 Question 9 Which of the following shows the length of the third side, in inches, of the triangle below? A right triangle is shown. One side of the triangle is labeled as 74 inches. The height of the triangle is labeled as 24 inches. Square root of 6052 inches Square root of 50 inches Square root of 70 inches Square root of 98 inches Question 10 The length of the hypotenuse of a right triangle is 14 inches. If the length of one leg is 6 inches, what is the approximate length of the other leg? 11.5 inches 12.6 inches 15.2 inches 20.0 inches Question 11 The picture shows a sandwich box: A sandwich box is shown with a right triangle side. The right triangle has hypotenuse 12 cm and base 5 cm. What is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? 4.1 centimeters 7.0 centimeters 8.5 centimeters 10.9 centimeters Question 12 The picture below shows a pole and its shadow: A pole is shown with a right triangle side. The right triangle has hypotenuse 365 cm and base 27 cm. What is the height of the pole? 196 centimeters 244 centimeters 338 centimeters 364 centimeters Question 13 What is the height of a cone with a radius of 4 inches and of volume 8 cubic inches? Round your answer to the tenths place. 0.5 inch 1.4 inches 2.0 inches 4.0 inches Question 14 The map shows the location of a mall, library, and school in a city: Coordinate grid shown from negative 12 to positive 12 on x axis at intervals of 2, and negative 12 to positive 12 on y axis at intervals of 2. A triangle is shown with vertices labeled Library, Mall, and School. Library is the ordered pair negative 10, 10 , Mall is the ordered pair 10, 10, and School is the ordered pair 10 and negative 11. Sarah traveled from the school to the mall and then from the mall to the library. Bret traveled from the school to the library. How many miles did Sarah and Bret travel altogether? 12 miles 29 miles 41 miles 70 miles Question 15 What is the length of the unknown side of the right triangle? A right triangle with hypotenuse x and legs 7 and 24 7 24 25 31

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