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 #3 #, #2 #, and #22 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-10-10T06:24:24

#22sqrt5#

Let's write what we know of the triangle
A=3
C=2

Since its a right triangle and A is the hypotenuse, we can apply Pythagoras' Theorem, so:
#A^2=B^2+C^2#
#3^2=B^2+2^2#
#B^2=9-4#
#B=sqrt(5)#

Now for the rectangle.
Its sides are B and 22 and its areas is B*22. Since #B=sqrt(5)#, the area of the rectangle is #color(blue)(22sqrt(5))#