the length of a rectangle is 7 times as long as its width. if the perimeter is 72 meters what is the length and width of the rectangle? please show how to set up eqaution.
L=7W
2L+2W=72
2(7W)+2W=72
14W+2W=72
16W=72
W=4.5, now substitute that back in either original equation to solve for L and
L=31.5
Substitute in both original equations, both work.
To solve this problem, let's represent the width of the rectangle as 'w' (in meters).
Since the length is 7 times as long as the width, we can represent the length as '7w' (in meters).
The formula for the perimeter of a rectangle is P = 2(length + width). In this case, the perimeter is given as 72 meters. So we can write the equation as:
72 = 2(7w + w)
Simplifying this equation, we get:
72 = 2(8w)
Divide both sides of the equation by 2:
36 = 8w
Now, divide both sides of the equation by 8:
4.5 = w
So, the width of the rectangle is 4.5 meters.
To find the length, substitute the value of 'w' into the equation for length:
Length = 7w = 7 * 4.5 = 31.5 meters
Therefore, the length of the rectangle is 31.5 meters and the width is 4.5 meters.