Final answer:
To find the area of the rectangle, we can set up a system of equations using the given information and use algebraic methods to solve for the width and length. The area is calculated by multiplying the length and width together.
Step-by-step explanation:
To solve this problem, we can set up a system of equations that represents the given information. Let's define the width of the rectangle as 'w' inches. The length would then be '2w + 3' inches, since it is 3 inches longer than twice the width. We know that the perimeter of a rectangle is calculated by adding up all four sides, so we can set up an equation:
2w + 2(2w + 3) = 126
Simplifying the equation:
2w + 4w + 6 = 126
Combining like terms:
6w + 6 = 126
Subtracting 6 from both sides:
6w = 120
Dividing both sides by 6:
w = 20
Now that we know the width is 20 inches, we can calculate the length of the rectangle:
2w + 3 = 2(20) + 3 = 43
The area of the rectangle is given by multiplying the length and width:
A = length × width = 43 × 20 = 860 square inches
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