Answer :
Let the length of the rectangle be [tex]$L$[/tex] and the width be [tex]$W$[/tex]. We are given that [tex]$W = 6$[/tex] inches and the perimeter [tex]$P = 42$[/tex] inches.
The perimeter of a rectangle is given by the formula:
[tex]$$
P = 2(L + W)
$$[/tex]
Substitute the known values into the formula:
[tex]$$
42 = 2(L + 6)
$$[/tex]
Divide both sides of the equation by 2 to simplify:
[tex]$$
21 = L + 6
$$[/tex]
Subtract 6 from both sides to solve for [tex]$L$[/tex]:
[tex]$$
L = 21 - 6 = 15
$$[/tex]
Thus, the length of the rectangle is [tex]$\boxed{15}$[/tex] inches.
The perimeter of a rectangle is given by the formula:
[tex]$$
P = 2(L + W)
$$[/tex]
Substitute the known values into the formula:
[tex]$$
42 = 2(L + 6)
$$[/tex]
Divide both sides of the equation by 2 to simplify:
[tex]$$
21 = L + 6
$$[/tex]
Subtract 6 from both sides to solve for [tex]$L$[/tex]:
[tex]$$
L = 21 - 6 = 15
$$[/tex]
Thus, the length of the rectangle is [tex]$\boxed{15}$[/tex] inches.
