Question

A rectangular Corn Hole area at the Recreation Center has a width of 5 feet and a length of 10 feet. If

Answer 1

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

$(5+x)(10+x)=84$

solve for x

Apply distributive property

$50+ 5x+10x+x^2=84\\x^2+15x-34=0$

solve the quadratic c equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^2+15x-34=0$  

so

$a=1\\b=15\\c=-34$

substitute in the formula

$x=\frac{-15\pm\sqrt{15^{2}-4(1)(-34)}} {2(1)}$

$x=\frac{-15\pm\sqrt{361}} {2}$

$x=\frac{-15\pm19} {2}$

$x=\frac{-15\pm19} {2}=2$

$x=\frac{-15\pm19} {2}=-17$

therefore

The solution is x=2 ft