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 #8 #, #2 #, and #14 #, respectively. What is the rectangle's area?
1 Answer
May 21, 2016
≈ 108.44 square units
Explanation:
Here is a sketch (not to scale)
Area of rectangle = 14B
To calculate this area we require to find B.
Since the triangle is right with hypotenuse A, then we can use
#color(blue)" Pythagoras' theorem"" to calculate B"# For the given triangle :
#A^2=B^2+C^2#
#rArrB^2=A^2-C^2=8^2-2^2=64-4=60# now
#B^2=60rArrB=sqrt60# area of rectangle
#=14B=14xxsqrt60≈108.44" square units"#
