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 #9 #, #4 #, and #8 #, respectively. What is the rectangle's area?
1 Answer
Mar 5, 2016
Explanation:
To calculate the area of the rectangle , we require to find the length of side B . This can be done using
#color(blue) " Pythagoras's theorem "# In the right triangle:
#A^2 = B^2 + C^2 # hence
#B^2 = A^ 2 - C^2 = 9^2 - 4^2 = 81 - 16 = 65# now
#B^2 = 65 rArr B = sqrt65 # thus area of rectangle =
#8xxsqrt65 = 8sqrt65 ≈ 64.5 #
