Question

1. Find the value of x and the perimeter of the square.
2X
7x - 15

Answer 1

A square has 4 congruent side lengths. This means that each side will be the same length. Therefore, we can set the two lengths equal to each other.

`S=S`

`7x-15=2x`

Isolating a variable: rearranging an equation so that the variable is by itself

• done by performing inverse operations

3 Step Solving process:

1. Collect like terms

2. Perform inverse operations

3. Simplify if necessary

`7x-2x-15=0`

`5x=15`

`(5x)/(5)=(15)/(5)`

`x=3`

The value of x = 3

The perimeter can be found by adding all of the side lengths. A square has 4 sides.

a + a + a + a = P

However, we know that a square has congruent sides so we can manipulate this formula:

4a = P - where a is equal to the side length

Using a previous equation we know that a side length is equal to 2x and we know the value of x, to be 3. Therefore, a side length must be 6.

we can now input the value of the side length into the formula.

`4(6)=P`

`24=P`

The perimeter of the square is 24.