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 #16 #, #4 #, and #5 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-04-01T07:33:57

#20sqrt15#

Consider the diagram

enter image source here

Use the pythagorean theorem to find #c#

#color(blue)(a^2+b^2=c^2#

Where #c# is the Hypotenuse and #a,b# are the other two sides

#rarr4^2+b^2=16^2#

#rarr16+b^2=256#

#rarrb^2=256-16#

#rarrb^2=240#

#color(green)(rArrb=sqrt240=sqrt(16*15)=4sqrt15#

Now we need to find the area of the rectangle,Use

#color(blue)(Area=l*b#

Where #l and b# are the sides of the rectangle

So,Area=

#rarr4sqrt15*5#

#color(green)(rArr=20sqrt15#