Question

The length of a rectangle is 2 Inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x + 2) = 24, where x isthe width in inches, represents this situation.The value of x from the set {1,3,5,7} that holds true for the equation is ___.So, the width of the rectangle is___ Inches and its length is ___Inches

Answer 1

Question:

Solution:

Let the following equation:

`2x+2\mleft(x+2\mright)=24`

if we evaluate this equation at x=5, we obtain:

`2(5)+2\mleft(5+2\mright)=24`

this is equivalent to:

`10+2\mleft(7\mright)=24`

this is equivalent to:

`10\text{ + 14=24}`

that is:

`24\text{ = 24}`

so, if x = 5, then the equation holds. So that, we can conclude that the correct answer is:

The value of x from the set {1,3,5,7} that holds true for the equation is 7.

So, the width of the rectangle is 7 inches

and its length is 7 + 2 = 9 inches.