Question

find the value of $x$ for each of the squares shown below:

1. perimeter = 36cm

$2x + 3$

1. perimeter = 4cm

$3x - 11$

1. perimeter = 20cm

$4x - 3$

1. perimeter = 42cm

$5x + 3$

1. perimeter = 8cm

$2x - 3$

1. perimeter = 26cm

$3x - 4$

find the value of $x$ for each of the rectangles shown below:

1. perimeter = 40cm

$5x - 1$
$4x + 3$

1. perimeter = 50cm

$4x + 5$
$3x - 1$

1. perimeter = 29cm

$2x - 2$
$7x + 3$

1. perimeter = 44cm

$3x + 4$
$5x - 3$

Explanation:

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Squares:

1) Step1: Set perimeter formula for square

Perimeter of square: $4 \times \text{side length} = 36$
$\implies 4(2x + 3) = 36$

Step2: Simplify and solve for x

Divide both sides by 4: $2x + 3 = 9$
Subtract 3: $2x = 6$
Divide by 2: $x = 3$

2) Step1: Set perimeter formula for square

$4(3x - 11) = 4$

Step2: Simplify and solve for x

Divide by 4: $3x - 11 = 1$
Add 11: $3x = 12$
Divide by 3: $x = 4$

3) Step1: Set perimeter formula for square

$4(4x - 3) = 20$

Step2: Simplify and solve for x

Divide by 4: $4x - 3 = 5$
Add 3: $4x = 8$
Divide by 4: $x = 2$

4) Step1: Set perimeter formula for square

$4(5x + 3) = 42$

Step2: Simplify and solve for x

Divide by 4: $5x + 3 = \frac{21}{2}$
Subtract 3: $5x = \frac{21}{2} - \frac{6}{2} = \frac{15}{2}$
Divide by 5: $x = \frac{3}{2} = 1.5$

5) Step1: Set perimeter formula for square

$4(2x - 3) = 8$

Step2: Simplify and solve for x

Divide by 4: $2x - 3 = 2$
Add 3: $2x = 5$
Divide by 2: $x = 2.5$

6) Step1: Set perimeter formula for square

$4(3x - 4) = 26$

Step2: Simplify and solve for x

Divide by 4: $3x - 4 = \frac{13}{2}$
Add 4: $3x = \frac{13}{2} + \frac{8}{2} = \frac{21}{2}$
Divide by 3: $x = \frac{7}{2} = 3.5$
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Rectangles:

1) Step1: Set perimeter formula for rectangle

Perimeter of rectangle: $2(\text{length} + \text{width}) = 40$
$\implies 2[(5x - 1) + (4x + 3)] = 40$

Step2: Simplify and solve for x

Simplify inside brackets: $2(9x + 2) = 40$
Divide by 2: $9x + 2 = 20$
Subtract 2: $9x = 18$
Divide by 9: $x = 2$

2) Step1: Set perimeter formula for rectangle

$2[(4x + 5) + (3x - 1)] = 50$

Step2: Simplify and solve for x

Simplify inside brackets: $2(7x + 4) = 50$
Divide by 2: $7x + 4 = 25$
Subtract 4: $7x = 21$
Divide by 7: $x = 3$

3) Step1: Set perimeter formula for rectangle

$2[(2x - 2) + (7x + 3)] = 29$

Step2: Simplify and solve for x

Simplify inside brackets: $2(9x + 1) = 29$
Divide by 2: $9x + 1 = 14.5$
Subtract 1: $9x = 13.5$
Divide by 9: $x = 1.5$

4) Step1: Set perimeter formula for rectangle

$2[(3x + 4) + (5x - 3)] = 44$

Step2: Simplify and solve for x

Simplify inside brackets: $2(8x + 1) = 44$
Divide by 2: $8x + 1 = 22$
Subtract 1: $8x = 21$
Divide by 8: $x = \frac{21}{8} = 2.625$
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Answer:

Squares:

1. $x = 3$
2. $x = 4$
3. $x = 2$
4. $x = 1.5$
5. $x = 2.5$
6. $x = 3.5$

Rectangles:

1. $x = 2$
2. $x = 3$
3. $x = 1.5$
4. $x = 2.625$