Question

13 in the figure shown below, each pair of intersecting line segments meets at a right angle, and all the lengths are given in inches. what is the perimeter, in inches, of the figure?

1. of the 517 graduating seniors at brighton high school, approximately \\( \frac { 4 } { 5 } \\) will be attending college, and approximately \\( \frac { 1 } { 2 } \\) of those going to college will be attending a state college. which of the following is the closest estimate of the number of graduating seniors who will be attending a state college?

Explanation:

Step1: Calculate the total horizontal length

The total horizontal length is \(14 + 2+4 = 20\) inches. Since there are two horizontal sides (top - bottom pairs in perimeter calculation), the contribution of horizontal sides to the perimeter is \(2\times20\) inches.

Step2: Calculate the total vertical length

The total vertical length is \(5 + 4+3=12\) inches. Since there are two vertical sides (left - right pairs in perimeter calculation), the contribution of vertical sides to the perimeter is \(2\times12\) inches.

Step3: Calculate the perimeter

The perimeter \(P=2\times(20 + 12)\). First, \(20+12 = 32\), then \(2\times32=64\). But we made a mistake above. Let's use another approach.
We can also count each side:
The sum of all horizontal sides: \(14+(14 - 2-4)+2 + 4=20\) (re - arranging terms). The sum of all vertical sides: \(5+(5 + 4)+(5 + 4+3)=12\) (re - arranging terms).
Perimeter formula for a polygon (sum of all sides).
The sum of horizontal sides: \(14+(14-(2 + 4))+2+4=20\). The sum of vertical sides: \(5+(5 + 4)+(5+4 + 3)=12\).
Perimeter \(P=(14+(14-(2 + 4))+2 + 4)+(5+(5 + 4)+(5+4 + 3))+(4+(4+(2)))\) (counting all sides one - by - one).
Another way: Translate the sides. The figure can be "transformed" (by moving the inner horizontal and vertical sides) into a rectangle - like shape.
The equivalent length \(L=14+(2 + 4)=20\) and the equivalent width \(W=5+(4 + 3)=12\).
Perimeter of a rectangle \(P = 2(L + W)\). So \(P=2\times(20+12)=64\). Wait, no. Let's count each side:
Horizontal sides: \(14+(14-(2 + 4))+2+4=20\) (left - to - right). Vertical sides: \(5+(5 + 4)+(5+4 + 3)=12\) (top - to - bottom). Also, we have two more sides (the non - overlapping parts in the "notch"): \(4+(4+(2))\).
Wait, correct way:
Sum of all horizontal lengths: \(14+(14-(2 + 4))+2+4=20\) (left - to - right). Sum of all vertical lengths: \(5+(5 + 4)+(5+4 + 3)=12\) (top - to - bottom). And we have two more vertical segments of length \(4\) and two more horizontal segments of length \(4\) (from the "steps").
Perimeter \(P=(14+(14-(2 + 4))+2 + 4)+(5+(5 + 4)+(5+4 + 3))+4 + 4\)
\(P=(14 + 8+2 + 4)+(5+9 + 12)+4 + 4\)
\(P=(28)+(26)+8\)
\(P = 62\)

Answer:

E. 62