Question

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

Answer 1

2(x + 60) + 2(30) = 200

2x + 120 + 60 = 200

2x + 180 = 200

2x = 20

x = 10 ft

Answer 2

A) 10

Explanation:

Given:

Perimeter of rectangular backyard = 200 ft.

Width = 30 ft

Length =
`x+60`

We need to find the value of x.

Now we know that perimeter of rectangle is equal to twice the sum of its length and width.

Framing in equation form we get;

Perimeter of Rectangle =
`2(length+width)`

Substituting the given values we get;

`2(x+60+30)=200`

Using Addition Property we get;

`2(x+90)=200`

Using Distributive property we get;

`2x+2*90=200\\2x+180=200\\`

Now Using Subtraction property we will subtract 1800 on both side we get;

`2x+180-180=200-180\\2x=20`

Now we will use division property and divide both side by 2 we get;

`(2x)/(2)=(20)/(2)\\\\x=10\ ft`

Hence The value of x is 10 ft.