9514 1404 393
Answer:
12 by 16 meters
Step-by-step explanation:
The only Pythagorean triple that is an arithmetic sequence is (3, 4, 5), where the hypotenuse is 5 times the common difference.
The fact that the diagonal of the room is 5 times the difference in dimensions suggests that the ratios of sides to each other and the diagonal is 3 : 4 : 5, with a scale factor of 4 meters.
The room is 12 m wide by 16 m long.
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If you wish, you can write an equation that uses the Pythagorean theorem to relate width, length, and diagonal.
w² +(w+4)² = 20²
2w² +8w +16 = 400
w² +4w - 192 = 0 . . . . divide by 2, put in standard form
(w +16)(w -12) = 0 . . . . factor
The values of w that make this true are -16 and +12. A negative dimension is not realistic, so ...
the room is 12 m wide by 16 m long
