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 #7 #, #4 #, and #12 #, respectively. What is the rectangle's area?
1 Answer
May 7, 2016
≈ 68.93 square units
Explanation:
Here is a sketch (not to scale)
The area of the rectangle = 12B
To calculate the area we require to know the value of B.
Since the triangle is right, we can find B using
#color(blue)" Pythagoras' theorem "# The hypotenuse is A hence
#A^2=B^2+C^2# and rearranging we get
#B^2=A^2-C^2=7^2-4^2=33# now
#B^2=33rArrB=sqrt33# area of rectangle
#=12B=12xxsqrt33 ≈ 68.93" square units "#
