Question

practice #3

1. create an equation for the perimeter of the shape.
2. solve the equation for the value of x.

x =
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1. label all of the side lengths.

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diagram: rectangle with sides 5x, 7x-3, 5x, 7x-3, p=36

Explanation:

1. Create an equation for the perimeter of the shape.

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( 7x - 3 \) and the width is \( 5x \).

Step2: Substitute values into formula

Substitute length \( = 7x - 3 \) and width \( = 5x \) into the perimeter formula:
\( P = 2\times((7x - 3) + 5x) \)
Simplify the expression inside the parentheses: \( (7x - 3) + 5x = 12x - 3 \)
Then, \( P = 2\times(12x - 3) = 24x - 6 \)
We know \( P = 36 \), so the equation is \( 24x - 6 = 36 \).

Step1: Add 6 to both sides

Start with the equation \( 24x - 6 = 36 \). Add 6 to both sides to isolate the term with \( x \):
\( 24x - 6 + 6 = 36 + 6 \)
Simplify: \( 24x = 42 \)

Step2: Divide by 24

Divide both sides by 24 to solve for \( x \):
\( x = \frac{42}{24} \)
Simplify the fraction by dividing numerator and denominator by 6: \( x = \frac{7}{4} = 1.75 \)

Step1: Find length of \( 5x \) sides

Substitute \( x = \frac{7}{4} \) into \( 5x \):
\( 5\times\frac{7}{4} = \frac{35}{4} = 8.75 \)

Step2: Find length of \( 7x - 3 \) sides

Substitute \( x = \frac{7}{4} \) into \( 7x - 3 \):
\( 7\times\frac{7}{4} - 3 = \frac{49}{4} - \frac{12}{4} = \frac{37}{4} = 9.25 \)

So the side lengths are \( 5x = 8.75 \) (two sides) and \( 7x - 3 = 9.25 \) (two sides).

Answer:

\( 24x - 6 = 36 \)

2. Solve the equation for the value of \( x \).