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
Jim G.
May 21, 2016

≈ 108.44 square units

Explanation:

Here is a sketch (not to scale)

enter image source here

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"

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