The living room in a new house has the dimensions shown. What is the volume of the room?
1 answer:
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Answer:
A
Step-by-step explanation:
The side lengths must satisfy the Pythagorean Theorem to be a right triangle. The formula is where a is the smallest side, b is the medium side, and c is the largest side. Test each set of numbers.
This satisfies the theorem. Since this is a multiple choice question, only one solution is possible. A is the solution.
See the attached diagram, it has all the information you need.
(a) If the green radii are all 1, then the orange diameters are all 2 + √2, so that the orange radii are (2 + √2)/2 = 1 + √2/2.
This is because we can join the radii of two adjacent green circles to form the sides of a square with side length equal to twice the radius - i.e. the diameter - of the green circles. The diagonal of any square occurs in a ratio to the side length of √2 to 1. Then we get the diameter of an orange circle by summing this diagonal length and two green radii, and hence the radius by dividing this by 2.
(b) We get the blue diameter in the same way. It has length (2 + √2) (1 + √2/2) = 3 + 2√2, so that the blue radius is (3 + 2√2)/2 = 3/2 + √2.
