When Keisha installed a fence along the 200-foot perimeter of her rectangular back yard, she left an opening for a gate. In the diagram below, she used x to represent the length, in feet, of the gate. What is the value of x?

Accepted Solution

Hello!The answer is:The value of "x" is 10 feet.Why?To find the correct answer to this problem, we need to remember the formula to calculate the perimeteer of a rectangle, it's given by the following equation:[tex]Perimeter=2length+2width[/tex]Now, we are given that:[tex]Perimeter=200feet\\Width=30\\Length=x+60[/tex]Then, substituting into the equation, we have:[tex]200feet=2(x+60feet)+2*(30feet)[/tex]Applying the distributive property, we have:[tex]200feet=2x+120feet+60feet[/tex][tex]200feet-120feet-600feet=2x[/tex][tex]2x=200feet-120feet-60feet\\\\x=\frac{20feet}{2}=10feet[/tex]Hence, the length of the gate is 10feet.Have a nice day!