Pythagorean and Volume

Jenna wants to hang outdoor stringed lights on her house along the roofline and horizontally across the side of her house, connecting the ends of the roofline to create a triangle. What is the approximate total length, in feet, of the lights that she needs to create one triangle?

• A. 48

• B. 64

• C. 80

• D. 98

For a classroom party, there are 12 bottles of fruit punch. Each bottle is filled with 850 cubic centimeters of punch. The fruit punch will be served in cone-shaped paper cups that are 7 centimeters across and 12 centimeters tall. How many completely full cone-shaped cups of punch can be poured?

• A. 16

• B. 66

• C. 232

• D. 265

Look at the right triangle on the coordinate grid. What is the length of the hypotenuse?

• √11

• √24

• √55

• √73

The coordinate grid shows right triangle ABC and point D. What is the distance, in units, from point A to point D?

• A. √7

• B. √14

• C. 5

• D. 7

A right triangle is shown in the diagram below. Based on the Pythagorean Theorem, which statement is correct?

• The empty square has a side length of 8 and an area of 64 square units.

• The empty square has a side length of 9.6 and an area of 92 square units.

• The empty square has a side length of 10 and an area of 100 square units.

Which statement is an important part of the proof of the converse of the Pythagorean theorem?

• It must be assumed that the Pythagorean theorem is true.

• It must be assumed that the sum of the lengths of any two sides of a triangle are less than the length of the third side.

• It must be assumed that the Pythagorean theorem is false.

• It must be assumed that the sum of the lengths of any two sides of a triangle are greater than the length of the third side.

This figure is used as part of a visual description of an algebraic statement. Which of the following can be that algebraic statement?

• a^2 + b^2 = c^2 - The figure represents the Pythagorean theorem.

• \frac{1}{2} (a + b) = c - This equation is an incorrect formula for the area of the right triangle.

• a \div b = c - This equation can be used to represent the area of a rectangle, but it has no meaning for this figure.

• a^2 \cdot b^2 = c^2 - This equation resembles the Pythagorean theorem, but it uses multiplication instead of addition.

A new highway was built outside of Tri Town to relieve traffic on Route 1. How many miles are saved by traveling on the new highway to get from point A to point B?

• 1 mile

• 4 miles

• 13 miles

• 30 miles

A ladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall. Use this information to find how high above the ground the ladder meets the wall.

• √194 m

• 13 m

• 12 m

• 8 m

What is the volume of this firework? Use 3.14 for π. Round the answer to the nearest tenth.

• 58.0 cubic inches

• 72.2 cubic inches

• 144.4 cubic inches

• 182.1 cubic inches