Answer:
2 feet
Step-by-step explanation:
Let
x ----> the uniform amount added to each side
we know that
The algebraic expression that represent this situation is
[tex](5+x)(10+x)=84[/tex]
solve for x
Apply distributive property
[tex]50+ 5x+10x+x^2=84\\x^2+15x-34=0[/tex]
solve the quadratic c equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^2+15x-34=0[/tex]
so
[tex]a=1\\b=15\\c=-34[/tex]
substitute in the formula
[tex]x=\frac{-15\pm\sqrt{15^{2}-4(1)(-34)}} {2(1)}[/tex]
[tex]x=\frac{-15\pm\sqrt{361}} {2}[/tex]
[tex]x=\frac{-15\pm19} {2}[/tex]
[tex]x=\frac{-15\pm19} {2}=2[/tex]
[tex]x=\frac{-15\pm19} {2}=-17[/tex]
therefore
The solution is x=2 ft
