You are painting the roof of a boathouse. You are going to place the base of a ladder 3.2 feet from the boathouse. How long does the ladder need to be to reach the roof of the boathouse?
A. 2.2 ft
B. 12.6 ft
C. 15.6 ft
D. 3.2 ft
A box shaped like a right rectangular prism measures 5 centimeters by 2 centimeters by 3 centimeters. What is the length of the interior diagonal of the prism to the nearest hundredth?
A. 5.10 cm
B. 6.01 cm
C. 7.07 cm
D. 8.06 cm
A wall 12 feet long makes a corner with a wall that is 14 feet long. The other ends of the walls are about 18.44 feet apart. Do the walls form a right angle? Explain.
A. Yes, they form a right angle.
B. No, they do not form a right angle.
C. Cannot be determined.
D. More information is needed.
A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 2 feet. The slant height is 2 feet. What is the height of the heater? Round to the nearest tenth of a foot.
A. 1.0 ft
B. 1.4 ft
C. 1.7 ft
D. 1.8 ft
Analyze and Persevere: What is the measurement of the longest side in the right rectangular prism shown? Describe what you did to find it. Round to the nearest tenth of a centimeter.
A. 6.5 cm
B. 7.1 cm
C. 8.3 cm
D. 9.0 cm
Felipe is making triangles for a rectangle stained-glass window. He made the design shown, but wants to change it. Felipe wants to move the purple triangle to the corner. The purple piece has side lengths of 4.5 inches, 6 inches, and 7 inches. Can the purple piece be moved to the corner? Explain.
A. Yes, it can be moved.
B. No, it cannot be moved.
C. Depends on the dimensions.
D. Further information is required.
1. Ladder Length to Roof:
To find the length of the ladder, we can use the Pythagorean theorem, which states ( a^2 + b^2 = c^2 ), where ( c ) is the hypotenuse (the ladder), and ( a ) and ( b ) are the two other sides of the triangle. Here, ( a = 3.2 ) ft (the distance from the boathouse) and ( b ) needs to be the height of the roof, which we can assume is at least greater than zero to consider practical usage of the ladder.
However, without the height of the boathouse, we can’t calculate the length directly. Based on given choices, if you can clarify or assume a height, we can proceed.
Answer:
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2. Interior Diagonal of the Prism:
To find the interior diagonal ( d ) of the rectangular prism, use the formula:
[ d = sqrt{l^2 + w^2 + h^2} ]
where ( l = 5 ) cm, ( w = 2 ) cm, and ( h = 3 ) cm.
Calculating:
[ d = sqrt{5^2 + 2^2 + 3^2} = sqrt{25 + 4 + 9} = sqrt{38} approx 6.