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 #5 #, #4 #, and #11 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-03-06T06:02:12

The area of the rectangle is #33#.

From the data given we can draw the following shape:

Self-drawn
Since the triangle is right angled, we can determine the length of B using the Pythagorean theorem.

#B^2+C^2=A^2#

#B^2+4^2=5^2#

#B^2+16=25#

Subtract #16# from each side.

#B^2=25-16#

#B^2=9#

Determine the square root.

#B=3#

Since we know that #B=3# and that the side adjacent to #B# is #11#, the area of the rectangle can be calculated using the formula:

#A=lxxh#

where #l=#length (#11#) and #h=#height (in this case: #B=11#)

#A=3xx11#

#A=33#