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 :)
L + 1 = W
2L + 2W = 106 (perimeter)
Substitute L+1 for W in the second equation and solve for L. Insert that value into the first equation to solve for W. Check by putting both values into the second equation.
Well, it seems like you've been juggling numbers there! Let's solve this puzzle together, shall we?
Let's say the width of the rectangle is "w" cm. According to the problem, the length is 1 cm less than the width, so the length would be "w - 1" cm.
Now, we can use the formula for the perimeter of a rectangle, which is 2 times the width plus 2 times the length. In this case, it would be:
2w + 2(w - 1) = 106
Simplifying that equation, we get:
2w + 2w - 2 = 106
4w - 2 = 106
4w = 108
Now, divide both sides of the equation by 4:
w = 108 / 4
w = 27
So, the width of the rectangle is 27 cm. And since the length is 1 cm less than the width, the length would be 26 cm.
Therefore, the dimensions of the rectangle are 27 cm by 26 cm. Ta-da!
I hope that helps, and remember, next time don't get too carried away with those numbers. Keep calm and solve on!
Sure! Let's solve the problem step by step.
Let's assume the width of the rectangle is x cm. According to the problem, the length of the rectangle is 1 cm less than its width. So the length can be written as (x-1) cm.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
Given that the perimeter of the rectangle is 106 cm, we can write the equation as:
106 = 2((x-1) + x)
Now, let's solve this equation to find the value of x.
Simplifying the equation:
106 = 2(2x - 1)
106 = 4x - 2
108 = 4x
x = 27
So, the width of the rectangle is 27 cm.
To find the length, substitute the value of x back into the expression for length:
Length = x - 1 = 27 - 1 = 26 cm
Therefore, the dimensions of the rectangle are: Width = 27 cm and Length = 26 cm.
Sure! I'd be happy to help you solve this problem.
Let's start by assigning variables to represent the dimensions of the rectangle. Let's say the width is "w" cm. Since the length of the rectangle is 1 cm less than its width, we can express the length as "w - 1" cm.
Given that the perimeter of the rectangle is 106 cm, we can write an equation to represent this information:
Perimeter = 2(length + width)
Plugging in the values, we get:
106 = 2((w - 1) + w)
Now, let's simplify the equation:
106 = 2(2w - 1)
106 = 4w - 2
Adding 2 to both sides of the equation:
106 + 2 = 4w
108 = 4w
To solve for "w," divide both sides of the equation by 4:
108/4 = w
27 = w
So, the width of the rectangle is 27 cm.
Now, to find the length, substitute the value of "w" back into the equation for the length:
Length = w - 1
Length = 27 - 1
Length = 26 cm
Therefore, the dimensions of the rectangle are width = 27 cm and length = 26 cm.