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 #10 #, #8 #, and #4 #, respectively. What is the rectangle's area?
1 Answer
Apr 8, 2016
24 square units
Explanation:
The area of the rectangle =
#color(blue)" 4B" # To calculate the value of the area , require to find B.
Since the triangle is right with hypotenuse A , we can use
#color(red)" Pythagoras' theorem " " to find B"#
# A^2 = B^2 +C^2 rArr B^2 = A^2 - C^2 #
#rArr B^2 = 10^2 - 8^2 = 100 - 64 = 36 # now
# B^2 = 36 rArr B = sqrt36 = 6 # and area of rectangle = 4B
# = 4xx6 = 24" square units "#
