the length of a rectangle is 7 meters more than twice the width. the perimeter is 68 meters. solve for length and width.
I need this step by step using the blueprint...please.
No blueprint available.
L = 2W + 7
2W + 2L = 68
Substitute 2W+7 for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
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he length of a rectangle is 7 meters more than twice the width. the perimeter is 68 meters. solve for length and width.
To solve for the length and width of the rectangle, we can use the given information that the length is 7 meters more than twice the width, and the perimeter is 68 meters.
Let's break down the problem step by step using the blueprint:
Step 1: Assign variables:
Let's assign variables to the length and width using the information given in the problem. Let:
- L be the length of the rectangle
- W be the width of the rectangle
Step 2: Translate the given information into equations:
Translate the given information into mathematical equations based on the variables we assigned.
According to the problem, the length (L) is 7 meters more than twice the width (W). Therefore, we can write the equation:
L = 2W + 7
The perimeter of a rectangle can be calculated by the formula:
Perimeter = 2(L + W)
In this case, the perimeter is given as 68 meters, so we can write the equation:
68 = 2(L + W)
Step 3: Solve the system of equations:
Now, we need to solve the system of equations, which consists of the two equations we derived in Step 2.
We have the equations:
L = 2W + 7
68 = 2(L + W)
Simplify the second equation by distributing the 2:
68 = 2L + 2W
To make the system easier to solve, we can express one of the variables in terms of the other.
From the first equation, we can rewrite it as:
L - 2W = 7
Now we have two equations:
L - 2W = 7
2L + 2W = 68
We can eliminate the W variable by adding the two equations together. Since (-2W + 2W = 0), the W variable cancels out, and we are left with:
3L = 75
Divide both sides of the equation by 3:
L = 25
Step 4: Substitute the value of L into one of the original equations to solve for W:
We can substitute the value of L (25) into the equation L = 2W + 7:
25 = 2W + 7
Subtract 7 from both sides:
18 = 2W
Divide both sides by 2:
W = 9
Step 5: Check the solution:
To check the solution, substitute the values of L and W into one of the original equations.
Using the equation L = 2W + 7:
25 = 2(9) + 7
25 = 18 + 7
25 = 25
The equation is true, which means the solution is correct.
Step 6: Answer the question:
The length (L) of the rectangle is 25 meters, and the width (W) is 9 meters.