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 #2 #, #1/3 #, and #3 #, respectively. What is the rectangle's area?
1 Answer
Mar 15, 2016
Explanation:
The area of the rectangle = 3B . To calculate this area , require to find length of B.
Since this is a right triangle , B can be found using#color(blue)" Pythagoras' theorem " # A is the hypotenuse hence
#A^2 = B^2 + C^2 # thus
# B^2 = A^2 - C^2 # here A = 3 and C
# = 1/3 # hence :
# B^2 = 2^2 - (1/3)^2 = 4 - 1/9 = 35/9 # now
# B^2 = 35/9 rArr B = sqrt(35/9) = 1/3sqrt35 # area of rectangle = 3B =
# 3xx1/3 sqrt35 = sqrt35 ≈ 5.916 #
