sydney is cutting the crust from the edges of her sandwich. the dimensions, in centimeters, of the sandwich…

sydney is cutting the crust from the edges of her sandwich. the dimensions, in centimeters, of the sandwich is shown. which expression represents the total perimeter of her sandwich, and if ( x = 1.2 ), what is the approximate length of the crust? ( 8x^{2}+34 ); 43.6 centimeters ( 8x^{2}+34 ); 45.52 centimeters ( 4x^{2}+17 ); 21.8 centimeters ( 4x^{2}+17 ); 22.76 centimeters

sydney is cutting the crust from the edges of her sandwich. the dimensions, in centimeters, of the sandwich is shown. which expression represents the total perimeter of her sandwich, and if ( x = 1.2 ), what is the approximate length of the crust? ( 8x^{2}+34 ); 43.6 centimeters ( 8x^{2}+34 ); 45.52 centimeters ( 4x^{2}+17 ); 21.8 centimeters ( 4x^{2}+17 ); 22.76 centimeters

Answer

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter formula for a rectangle is (P = 2(l + w)), where (l) is the length and (w) is the width. Here, (l=2x^{2}+9) and (w = 2x^{2}+8).

Step2: Substitute into the perimeter formula

[ \begin{align*} P&=2((2x^{2}+9)+(2x^{2}+8))\ &=2(2x^{2}+9 + 2x^{2}+8)\ &=2(4x^{2}+17)\ &=8x^{2}+34 \end{align*} ]

Step3: Substitute (x = 1.2) into the perimeter formula

When (x = 1.2), we have (P=8\times(1.2)^{2}+34). First, calculate ((1.2)^{2}=1.44). Then (8\times1.44 = 11.52). Finally, (P=11.52+34=45.52)

Answer:

(8x^{2}+34); (45.52) centimeters (the second option)