Arectangular room has a diagonal measure of 20 meters. the room is four meters longer than it is wide. find the room's dimensions

9514 1404 393

  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.

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

ratio is 2 : 9

the answer is three

13.5 : 3