I am havine trouble with this problem will someone please help me
The perimeter of a rectangle is 68m The length is 10 m more than twice the width. Find the dimensions
width= 8 m
length= 26 m
width --- x
length -- 2x + 10
solve 2x + 2(2x+10) = 68
to get Ana's anwers
Of course! Let's work through this problem step by step.
Let's start by assigning variables to the dimensions of the rectangle. Let's use "L" for length and "W" for width.
We know that the perimeter of a rectangle is given by the formula: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
From the problem statement, we are given that the perimeter of the rectangle is 68m. So we can equate the formula to 68:
2L + 2W = 68
We are also given that the length is 10m more than twice the width. In mathematical terms, this can be written as:
L = 2W + 10
Now we have a system of equations:
2L + 2W = 68
L = 2W + 10
To solve this system, we can use substitution or elimination method. Let's use substitution.
From the second equation, we can rewrite it as L - 2W = 10. Now we can substitute this expression for L in the first equation:
2(L - 2W) + 2W = 68
2L - 4W + 2W = 68
2L - 2W = 68
Now we have a simplified equation:
2L - 2W = 68
Next, we can divide this equation by 2:
L - W = 34
Now we have a new equation to work with:
L - W = 34
From the original second equation, L = 2W + 10, we can rewrite it as:
L - 2W = 10
Now we have a system of equations:
L - W = 34
L - 2W = 10
We can solve this system of equations using the method of elimination. We'll subtract the second equation from the first equation:
(L - W) - (L - 2W) = 34 - 10
L - W - L + 2W = 24
-W + 2W = 24
W = 24
Now that we have found the value of W (the width), we can substitute it back into one of the original equations to find L (the length).
Let's use L = 2W + 10:
L = 2(24) + 10
L = 48 + 10
L = 58
Therefore, the dimensions of the rectangle are:
Width (W) = 24m
Length (L) = 58m