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 #18 #, #15 #, and #9 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-01-19T08:03:51

Area of rectangle is #89.56#.

In the right angled triangle, as #A=18# is hypotenuse and #C=15#, we have side #B# given by Pythagoras theorem as

#sqrt(18^2-15^2)=sqrt(324-225)=sqrt99=3sqrt11#

We have rectangle adjacent to side #B#, hence one side of rectangle is #3sqrt11# and as other side of rectangle is #9#

Hence area of rectangle is

#9xx3sqrt11=27xx3.317=89.559~~89.56#.