Question 823933: A square and an equilateral triangle have the same height. The square has an area of 225 feet squared. What is the area of the triangle?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
square:
a = 225 = xx
x = 15
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triangle:
h = 15
s = sqrt( 15*15 + (s/2)(s/2) )
ss = 225 + ss/4
ss - ss/4 - 225 = 0
4ss/4 - ss/4 - 225 = 0
3ss/4 - 225 = 0
0.75ss - 225 = 0
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the above quadratic equation is in standard form, with a=0.75, b=0, and c=-225
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.75 0 -225
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
s = 17.3205081
s = -17.3205081
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negative length doesn't make sense for this problem, so use the positive root:
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answer:
triangle side = 17.3205081 ft
triangle area = 1/2(17.3205081)(15) = 129.9 sq.ft
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