Kate just bought a tv that measures 42 inches diagonally, and is 18 inches tall. She wants to place the tv into a 40 inch wide cabinet. Will the tv fit and if so, how much room will be left (width) in the cabinet after the tv is placed?

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  yes, about 2.05 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the width of the TV.

  w^2 +h^2 = d^2

  w = √(d^2 -h^2)

  w = √(42^2 -18^2) = √1440 = 12√10

  w ≈ 37.95 . . . inches

This dimension is less than 40 inches by a margin of ...

  40 -37.95 = 2.05 . . . inches

The TV will fit, with 2.05 inches of space remaining.

the answer is 8/21

hope this