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 #11 #, #6 #, and #13 #, respectively. What is the rectangle's area?

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Answer 1 · 2018-02-09T03:11:22

Area of rectangle #approx 120#

Given:
In triangle #ABC#
#A# is hypotenuse = 11
#C# = 6
So, B is the other side of the right angled triangle.
Let us find B using Pythagoras theorem:

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

#=> B^2 = A^2- C^2#

#=> B^2 =11^2 - 6^2#

#=> B^2 = 121-36 = 85#

#=> B = sqrt 85#

#=> B approx 9.22#

Also given the length of side of rectangle adjacent to B = 13

#=> # sides of rectangle are B =9.22 and adjacent side =13.
So, area of rectangle will be:

#therefore Area = 9.22 xx 13 = 119.86 approx 120#