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Can someone help me solve these please? thank you.

Can someone help me solve these please? thank you.-example-1

1 Answer

4 votes

Answer:

  1. DA = 24
  2. GS = 39
  3. 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.

Can someone help me solve these please? thank you.-example-1
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