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

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Answer 1 · 2016-03-12T09:08:02

#Area=5sqrt5#

Consider the diagram

enter image source here

We need to find the length #B#

#color(blue)(a^2+b^2=c^2#

Where

#color(red)(c=Hypoten##color(red)(use#

#color(red)(a andb=other# #color(red)(two# #color(red)(sides#

But, In this case #A# is the #Hypoten##use#

#:.2^2+B^2=3^2#

#rarr4+B^2=9#

#rarrB^2=9-4#

#rarrB^2=5#

#rArrB=sqrt5#

We find that #B# is one of the side of the rectangle

#Area# #of# #recta##ngl##e=l*b# #units#

#color(green)( :.Area=sqrt5*5=5sqrt5#