Question

1. in the figure shown below, each pair of intersecting line segments meets at a right angle, and all the lengths given are in inches. what is the perimeter, in inches, of the figure? a. 40 b. 52 c. 56 d. 66 e. 80

Explanation:

Step1: Analyze vertical side - lengths

The sum of vertical side - lengths: $(4 + 6+6 + 4)=20$. Since the figure has two sets of vertical side - lengths (left and right), the total for vertical sides is $2\times20 = 40$.

Step2: Analyze horizontal side - lengths

The sum of horizontal side - lengths: $(10 + 26)=36$. Since the figure has two sets of horizontal side - lengths (top and bottom), the total for horizontal sides is $2\times36\div2=36$ (we divide by 2 because each horizontal length is counted only once in the perimeter calculation for non - overlapping parts).

Step3: Calculate perimeter

The perimeter $P$ is the sum of vertical and horizontal side - lengths. $P=40 + 36=76$. But we made a mistake above. Let's use another approach.
We can use the fact that we can "rearrange" the sides. The horizontal lengths add up to $10 + 26=36$ and the vertical lengths add up to $4+6 + 4+6=20$. The perimeter is $2\times(36\div2)+2\times(20\div2)=36 + 20=56$.

Answer:

C. 56