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 #, #2/3 #, and #3 #, respectively. What is the rectangle's area?

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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 #, #2/3 #, and #3 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-03-01T08:54:11

#4sqrt(2)#

Explanation:

The area of a rectangle is #A = Base*Height# The base is given as #3# and the height is #B#. We can use Pythagoras' Theorem to calculate #B# because it is a right triangle and we have been given the lengths of the other two sides.

#A^2 = B^2 +C^2#
#B^2 = A^2 - C^2 = 2^2 - (2/3)^2#
#B^2 = 4 - 4/9 = 32/9#

#B = sqrt(32/9) = (4sqrt(2))/3#

Area #A = 3*(4sqrt(2))/3 = 4sqrt(2)#

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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 #, #2/3 #, and #3 #, respectively. What is the rectangle's area?

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