The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. find the width of the rectangle.
Let L represent the length of the rectangle in inches, and let W represent the width of the rectangle in inches.
According to the problem, the width is 6 inches less than 3 times the length, so we can write this as an equation:
W = 3L - 6
The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
In this case, the perimeter is 104 inches, so we can write:
104 = 2(L + W)
Now, substitute the expression for W from the first equation into the perimeter equation:
104 = 2(L + (3L - 6))
Simplify the equation:
104 = 2(4L - 6)
Now, distribute the 2 on the right side of the equation:
104 = 8L - 12
Add 12 to both sides of the equation to isolate the 8L term:
104 + 12 = 8L
116 = 8L
Now, divide both sides by 8 to find the value of L:
L = 116 / 8 L = 14.5
So, the length of the rectangle is 14.5 inches.
Now, use the first equation to find the width:
W = 3L - 6 W = 3(14.5) - 6 W = 43.5 - 6 W = 37.5
So, the width of the rectangle is 37.5 inches.
Related Question
View MorePromotion
Download Our Mobile Apps
