Answer:
- DA = 24
- GS = 39
- 9 inches
Explanation:
Given various quadrilaterals with side lengths marked, you want specific side lengths.
1. DA
Opposite sides of the parallelogram are the same length, so ...
5x -18 = 2x +12
3x = 30 . . . . . . . . . add 18-2x
x = 10
DA = 3x -6 = 3·10 -6 = 24
2. GS
All of the sides of a rhombus are the same length, so ...
3p -6 = 2p +9
p = 15 . . . . . . . . . . . add 6-2p
GS = 2p+9 = 2·15 +9 = 39
3. Shortest side
The perimeter is the sum of the side lengths.
46 = (x +8) +(2x +1) +(3x -6) +(4x -7)
46 = 10x -4
50 = 10x
5 = x
Then the side lengths are ...
- x+8 = 13
- 2x+1 = 11
- 3x-6 = 9
- 4x-7 = 13
The length of the shortest side is 9 inches.
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Additional comment
The attachment shows a graphical solution to the third problem. The lines y1–y4 are the side lengths as a function of x. The black line finds the value of x that makes the perimeter be 46. That value is 5. The vertical line at x = 5 intersects the other lines at their side length values. The bottom of these is the shortest side length: 9 inches when x=5.