Given the perimeter of this rectangle is 26 inches, solve for the value of x where the sides are x and x+3.
Understand the Problem
The question asks to find the value of 'x' given the perimeter of a rectangle is 26 inches, where the sides are 'x' and 'x+3'. We can solve this question by using the equation Perimeter = 2*(length + width).
Answer
$x = 5$
Answer for screen readers
$x = 5$
Steps to Solve
- Write the formula for the perimeter of a rectangle
The perimeter of a rectangle is given by $$P = 2 * (length + width)$$
- Substitute the given values
We know that perimeter $P = 26$, $length = x+3$, and $width = x$. Substituting these values into the formula: $$26 = 2 * (x + 3 + x)$$
- Simplify the equation
Simplify the expression inside the parentheses: $$26 = 2 * (2x + 3)$$
- Distribute the 2
Distribute the 2 on the right side of the equation: $$26 = 4x + 6$$
- Isolate the term with x
Subtract 6 from both sides of the equation: $$26 - 6 = 4x$$ $$20 = 4x$$
- Solve for x
Divide both sides by 4: $$\frac{20}{4} = x$$ $$x = 5$$
$x = 5$
More Information
The value of x represents one of the sides of the rectangle. Since $x=5$, one side is 5 inches long, and the other side is $x+3 = 5+3 = 8$ inches long.
Tips
A common mistake is not distributing the 2 correctly in the equation $26 = 2 * (2x + 3)$. Another mistake is forgetting to subtract 6 from both sides before dividing by 4.
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