I need help on this following problem: The length of a rectangle measures 1 cm less than its width. The perimeter of the rectangle is 106 cm. Find the dimensions of the rectangle. Now i have tried to solve this problem in multiple attempts as can be seen here: 54+53=107, 53+52=105, 48+49=97, 50+49=99. Can you please help me solve this or solve it for me please!! Either choice is appreciated :)
2(w + w-1) = 106
4w-2 = 106
4w = 108
w = 27
so, the width is 27 and the length is 26.
An odd way to assign the dimensions, I must say...
You forgot that the perimeter is twice the sum of the length and width.
Sure, I'd be happy to help you solve this problem! Let's break it down step by step.
Let's assume that the width of the rectangle is "w" centimeters.
According to the problem, the length of the rectangle measures 1 cm less than its width, so the length can be written as "w - 1" centimeters.
The perimeter of a rectangle is calculated by adding up all four sides. In this case, we have two equal-length sides (the width) and two equal-length sides (the length), so the perimeter is given by the equation:
2 * (width + length) = 106
Substituting the values we have:
2 * (w + (w - 1)) = 106
Simplifying the equation:
2 * (2w - 1) = 106
4w - 2 = 106
4w = 108
w = 108 / 4
w = 27
Now we know that the width of the rectangle is 27 centimeters.
To find the length, we substitute the value of the width back into one of the earlier equations:
Length = w - 1
Length = 27 - 1
Length = 26
So, the dimensions of the rectangle are width = 27 cm and length = 26 cm.