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 #14 #, #4 #, and #3 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-12-24T14:47:28

See a solution process below:

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The image above is the shapes we are dealing with from the question.

We can use the Pythagorean Theorem to find the length of #B#.

The Pythagorean Theorem states:

#B^2 + C^2 = A^2# where #A# is the hypotenuse of a right triangle.

Substituting the values from the problem and solving #B# gives:

#B^2 + 4^2 = 14^2#

#B^2 + 16 = 196#

#B^2 + 16 - color(red)(16) = 196 - color(red)(16)#

#B^2 + 0 = 180#

#B^2 = 180#

#sqrt(B^2) = sqrt(180)#

#B = sqrt(36 * 5)#

#B = sqrt(36)sqrt(5)#

#B = 6sqrt(5)#

The formula for the area of a rectangle is:

#A = l xx w#

Substituting the value from the problem and the value we calculated and calculating #A# gives:

#A = 6sqrt(5) xx 3#

#A = 18sqrt(5)#

Or

#A = 40.25# rounded to the nearest hundredth