Question 767524
Q:
A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the side that is shared with the square. Find the area of the square.
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A:
{{{drawing(200,200,-2,15,-2,15,line(0,0,sqrt(84),0),line(0,0,0,sqrt(84)),line(0,sqrt(84),sqrt(84),sqrt(84)),line(sqrt(84),sqrt(84),sqrt(84),0),line(sqrt(84),0,4+sqrt(84),0),line(sqrt(84),sqrt(84),4+sqrt(84),0),locate(sqrt(84),sqrt(21),"s"),locate(sqrt(84)+2,0,"4"), locate(2.5+sqrt(84),sqrt(21),"10"))}}}
Using Pythagorean Theorem:
{{{s^2 + 4^2 = 10^2}}}
{{{s^2}}} = {{{10^2 - 4^2}}} = {{{highlight(84)}}}.
The area of the square is {{{highlight(84)}}} {{{cm^2}}}