the length of a rectangle is 5 centimeters more than twice its width. if the perimeter of the rectangle is 94 centimeters, what are the length and width of the rectangle?
P = 2(W+L)
2[w+(2w+5)] = 94
w = 14
rectangle is 14x33
To find the length and width of the rectangle, we can set up a system of equations based on the given information.
Let's denote the width as "w" and the length as "l". We are told that the length is 5 centimeters more than twice the width, so we can write this as:
l = 2w + 5
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter. In this case, we know that the perimeter is 94 centimeters. So we can write this as:
94 = 2l + 2w
Now we have a system of equations:
l = 2w + 5
94 = 2l + 2w
We can solve this system of equations using substitution or elimination method.
Let's use substitution:
Substitute the first equation (l = 2w + 5) into the second equation:
94 = 2(2w + 5) + 2w
Simplify:
94 = 4w + 10 + 2w
Combine like terms:
94 = 6w + 10
Subtract 10 from both sides:
84 = 6w
Divide by 6:
w = 14
Now substitute the value of w back into the first equation to find l:
l = 2w + 5
l = 2(14) + 5
l = 28 + 5
l = 33
So the width of the rectangle is 14 centimeters, and the length is 33 centimeters.