A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #4 #, #6 #, and #9 #, respectively. What is the rectangle's area?

1 Answer
Alan P.
May 21, 2016

The given configuration can not exist. Please correct and re-submit.

Explanation:

The question claims that side A is the hypotenuse with a length of #4#. It is also claimed that side C of the same right triangle has a length of #6#.

The length of the hypotenuse of a right triangle must be greater than the length of either of the other sides.

Possible valid respective lengths:
#< A, C, "rectangle's side"> =#
#color(white)("XXX")<6,4,9>#, or
#color(white)("XXX")<9,6,4>#, or
#color(white)("XXX")<9,4,6>#

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Steps in solving this type of problem.

  1. Use the Pythagorean Theorem to find the length of side B: #sqrt(A^2-C^2)#
  2. Rectangle's area #=B xx "rectangle's side"#
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