Question 856
Let the length of one side of the square be x:
{{{ x^2 }}} is the area of the square
Area of the retangle:
(x+6)(x-1)
which is equal to
{{{ x^2+5x-6 }}}
so if the area of the retangle is twice the area of the square, then we can set up an equation:
{{{ x^2+5x-6=2x^2 }}}
Now, slove it:
{{{ x^2+5x-6-x^2=2x^2-x^2 }}}
{{{ 5x-6=x^2 }}}
{{{ 5x-6-x^2=x^2-x^2 }}}
{{{ -x^2+5x-6=0 }}}
Now use the quadratic formula to slove:
{{{x = ((-5) +- sqrt((-5^2)-4*(-1)*(-6))/(2*(-1)))}}}
{{{x = (((-5) +- sqrt((25-24)))/(-2))}}}
{{{x = (((-5)+- 1)/(-2))}}}
x = (-4/-2) or (-6/-2)
x = 2 or 3
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Check:
if x=2
x^2 = 4
(2+6)(2-1) = 8
8 = 2*4
8=8 (2 is right!)
if x=3
x^2 = 9
(3+6)(3-1) = 18
18 = 2*9
18=18 (3 is right!)
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So the answer is 2 or 3, they both work!