Question

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

a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount
added to each side?
5 ft x
10 ft

Answer 1

2 feet

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√(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