Rectangle Perimeter: Solving for x

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Questions and Answers

A rectangle has a length of $x + 3$ and a width of $x$. If the perimeter is 26 inches, which equation can be used to correctly solve for $x$?

  • $2x + 2(x+3) = 26$ (correct)
  • $4x + 3 = 26$
  • $x(x+3) = 26$
  • $x + (x+3) = 26$

A rectangular garden has a width of $x$ meters and a length of $x + 3$ meters. If the perimeter of the garden is 26 meters, what is the width ($x$) of the garden?

  • 5 meters (correct)
  • 6.5 meters
  • 10 meters
  • 8 meters

A rectangle has a perimeter of 26 inches. If the length is 3 inches more than the width, what is the area of the rectangle?

  • 16 square inches
  • 40 square inches (correct)
  • 36 square inches
  • 52 square inches

What is value of $x$ if a rectangle, with perimeter 26 inches, has one side with length $x$ and another side with length $x + 3$?

<p>5 (A)</p> Signup and view all the answers

A rectangle's length is represented by $x + 3$ and its width by $x$. If the perimeter of this rectangle is 26, what expression represents its area?

<p>$x^2 + 3x$ (B)</p> Signup and view all the answers

For a rectangle with perimeter of 26 inches, if the width is $x$ inches and the length is $x + 3$ inches, what inequality represents possible values of $x$?

<p>$x &gt; 0$ (B)</p> Signup and view all the answers

Consider a rectangle with one side measuring $x$ inches and the other $x + 3$ inches. Given the perimeter is 26 inches, if you increase $x$ by 1 inch, by how much does the perimeter increase?

<p>4 inches (B)</p> Signup and view all the answers

If the perimeter of a rectangle is 26 inches and its sides are $x$ and $x + 3$, what will the perimeter be if both $x$ and $x + 3$ are doubled?

<p>52 inches (C)</p> Signup and view all the answers

A rectangle has sides of length $x$ and $x + 3$. Given a perimeter of 26 inches, if the rectangle were unfolded into a straight line, how long would that line be?

<p>26 inches (D)</p> Signup and view all the answers

A rectangle with a perimeter of 26 has sides $x$ and $x+3$. If a square is constructed with the side length equal to $x$, what is the perimeter of that square?

<p>20 (C)</p> Signup and view all the answers

Flashcards

What is the perimeter of a rectangle?

The perimeter of a rectangle is the sum of all its sides. For a rectangle with length (l) and width (w), the perimeter (P) is given by P = 2l + 2w.

What equation do you use to solve for x?

Given a rectangle with sides x and x+3, and a perimeter of 26 inches, the equation to find x is: 2(x) + 2(x+3) = 26.

How to simplify the equation?

To solve: 2x + 2(x+3) = 26, first distribute: 2x + 2x + 6 = 26, then combine like terms: 4x + 6 = 26. Subtract 6 from both sides: 4x = 20. Finally, divide by 4.

How to solve for x?

After solving the equation 4x = 20, divide both sides by 4 to isolate x. This gives x = 5.

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What is the value of x?

The value of x is 5 inches.

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Study Notes

Rectangle Perimeter

  • The perimeter of a rectangle is 26 inches
  • Need to solve for the value of x
  • The width of the rectangle is x + 3
  • The height of the rectangle is x

Solving for x

  • The formula for the perimeter of a rectangle is P = 2w + 2h
  • Substituting the values: 26 = 2(x + 3) + 2(x)
  • Simplifying the equation: 26 = 2x + 6 + 2x
  • Combining like terms: 26 = 4x + 6
  • Subtracting 6 from both sides: 20 = 4x
  • Dividing by 4: x = 5

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