Question

sydney is cutting the crust from the edges of her sandwich. the dimensions, in centimeters, of the sandwich are length = (2x^2 + 8) and width = (2x^2 + 9). which expression represents the total perimeter of her sandwich, and if (x = 1.2)? options: (4x^2 + 17), (4x^2 + 72), (8x^2 + 34), (8x^2 + 72). what is the approximate length of the crust? 45.52 cm. (diagram: a rectangle labeled “sandwich” with length (2x^2 + 8) and width (2x^2 + 9))

Explanation:

First Sub - Question (Expression for Perimeter)

Step1: Recall Perimeter Formula for Rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). Here, length \( l=2x^{2}+8 \) and width \( w = 2x^{2}+9 \).

Step2: Substitute Length and Width into Formula

\( P=2\times((2x^{2}+8)+(2x^{2}+9)) \)

Step3: Simplify the Expression Inside the Parentheses

First, combine like terms: \( (2x^{2}+8)+(2x^{2}+9)=2x^{2}+2x^{2}+8 + 9=4x^{2}+17 \)

Step4: Multiply by 2

\( P = 2\times(4x^{2}+17)=8x^{2}+34 \) Wait, no, wait. Wait, no, let's re - do step 2 and 3. Wait, length is \( 2x^{2}+8 \), width is \( 2x^{2}+9 \). So \( \text{length}+\text{width}=(2x^{2}+8)+(2x^{2}+9)=4x^{2}+17 \). Then perimeter is \( 2\times(\text{length}+\text{width})=2\times(4x^{2}+17)=8x^{2}+34 \)? Wait, no, the options are \( 4x^{2}+17 \), \( 4x^{2}+72 \), \( 8x^{2}+34 \), \( 8x^{2}+72 \). Wait, maybe I made a mistake. Wait, no, the formula for the perimeter of a rectangle is \( P = 2l + 2w \), where \( l \) is length and \( w \) is width. So \( l = 2x^{2}+8 \), \( w=2x^{2}+9 \). Then \( 2l=2\times(2x^{2}+8)=4x^{2}+16 \), \( 2w = 2\times(2x^{2}+9)=4x^{2}+18 \). Then \( P=(4x^{2}+16)+(4x^{2}+18)=8x^{2}+34 \). So the expression for the perimeter is \( 8x^{2}+34 \).

Second Sub - Question (Perimeter when \( x = 1.2 \))

Step1: Substitute \( x = 1.2 \) into the Perimeter Formula

We have the perimeter formula \( P = 8x^{2}+34 \). Substitute \( x = 1.2 \) into it.

Step2: Calculate \( x^{2} \)

First, calculate \( x^{2}=(1.2)^{2}=1.44 \)

Step3: Calculate \( 8x^{2} \)

\( 8x^{2}=8\times1.44 = 11.52 \)

Step4: Calculate the Perimeter

\( P=11.52+34=45.52 \)

First Sub - Question Answer: \( 8x^{2}+34 \)

Second Sub - Question Answer: \( 45.52 \) cm

Answer:

Step1: Substitute \( x = 1.2 \) into the Perimeter Formula

We have the perimeter formula \( P = 8x^{2}+34 \). Substitute \( x = 1.2 \) into it.

Step2: Calculate \( x^{2} \)

First, calculate \( x^{2}=(1.2)^{2}=1.44 \)

Step3: Calculate \( 8x^{2} \)

\( 8x^{2}=8\times1.44 = 11.52 \)

Step4: Calculate the Perimeter

\( P=11.52+34=45.52 \)

First Sub - Question Answer: \( 8x^{2}+34 \)

Second Sub - Question Answer: \( 45.52 \) cm