Question

express the perimeter of the figure shown below in simplest form.
figure with labeled sides: top side 4x - 6, right side 2x - 4, a notch with horizontal side x + 1 and vertical side x + 3, bottom side 2x + 1, left side x + 13
a. 11x + 8
b. 11x + 28
c. 19x
d. 39x

Explanation:

Step1: Identify horizontal sides

Top: $4x - 6$; Bottom: $2x + 1 + x + 3 = 3x + 4$; Right: $x + 1$; Left: $x + 1$

Step2: Identify vertical sides

Left: $x + 13$; Right: $2x - 4 + x + 1 = 3x - 3$; Top: $2x - 4$; Bottom: $x + 13 - (2x - 4) = -x + 17$

Step3: Sum all sides

$(4x - 6) + (3x + 4) + (x + 1) + (x + 1) + (x + 13) + (3x - 3) + (2x - 4) + (-x + 17)$

Step4: Combine like terms

$4x+3x+x+x+x+3x+2x-x + (-6+4+1+1+13-3-4+17) = 11x + 28$

Answer:

B. 11x + 28