A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?
(A) 15
(B) 20
(C) 25
(D) 10√2
(E) 10√3
The OA is the option A.
How can I determine which one is the correct answer? Any help? Thanks.
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A rectangular box is 10 inches wide, 10 inches long
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The longest line that can be drawn inside a rectangular solid is called the MAIN DIAGONAL.M7MBA wrote:A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?
(A) 15
(B) 20
(C) 25
(D) 10√2
(E) 10√3
Use the SUPER-PYTHAGOREAN THEOREM.
If d = the length of the main diagonal, then:
d² = l² + w² + h².
In the problem above:
d² = 10² + 10² + 5²
d² = 225
d = 15.
The correct answer is A.
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The greatest possible distance between two points in a rectangular solid is the diagonal i.e.,the distance from the front upper left to the back lower right. We need to determine the diagonal of the rectangular solid, using the equation:M7MBA wrote:A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?
(A) 15
(B) 20
(C) 25
(D) 10√2
(E) 10√3
diagonal^2 = length^2 + width^2 + height^2
d^2 = 10^2 + 10^2 + 5^2
d^2 = 225
d = 15
Answer: A
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