A rectangle has a perimeter of 12x + 20 and a width of 2x + 8. What is the length of the rectangle?
let the length be l
2l + 2(2x+8) = 12x+20
2l = 8x + 4
l = 4x + 2
I skipped what I thought was an easy simplification ...
2l + 2(2x+8) = 12x+20
2l + 4x + 16 = 12x + 20
2l = 12x + 20 - 4x - 16
2l = 8x + 4
To find the length of the rectangle, we need to use the formula for the perimeter of a rectangle, which is given by the formula:
Perimeter = 2 × (Length + Width)
In this case, we have the perimeter given as 12x + 20 and the width as 2x + 8. We can substitute these values into the formula and solve for the length.
12x + 20 = 2 × (Length + (2x + 8))
Now, we can simplify and solve for the length:
12x + 20 = 2 × (Length + 2x + 8)
12x + 20 = 2 × Length + 4x + 16
12x - 4x = 2 × Length + 16 - 20
8x = 2 × Length - 4
To isolate the length, we subtract 2x from both sides:
8x - 2x = 2 × Length - 4 - 2x
6x = 2 × Length - 4
Next, we add 4 to both sides:
6x + 4 = 2 × Length - 4 + 4
6x + 4 = 2 × Length
Finally, we divide both sides by 2 to solve for Length:
(6x + 4) ÷ 2 = (2 × Length) ÷ 2
3x + 2 = Length
Therefore, the length of the rectangle is given by 3x + 2.