Question

Can you guys please do both with the work please and thank you if you actually do it

Answer 1

Answer:

  7.  29 cm

  8.  equation: 61 = (x) +(2x -7) +(3x +2); sides 11, 15, 35

Step-by-step explanation:

7. Let w represent the width. The length is 3 less than twice the width, so the length is 2w-3. The perimeter is given by the formula ...

  P = 2(L+W)

Substituting the known values, we have ...

  90 = 2((2w-3) +w)

  45 = 3w -3 . . . . . . . . divide by 2

  15 = w - 1 . . . . . . . . . .divide by 3

  16 = w . . . . . . . . . . . . add 1

  L = 2w -3 = 2(16) -3 = 29

The length of the rectangle is 29 cm.

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8. The equation that should be used is the one that relates the side lengths to the perimeter.

  P = a + b + c . . . . for sides a, b, c

  61 = (x) +(2x -7) +(3x +2)

  61 = 6x -5 . . . . . . collect terms

  66 = 6x . . . . . . . . add 5

  11 = x . . . . . . . . . . divide by 6

Then the side lengths are ...

  a = x = 11

  b = 2x -7 = 2(11) -7 = 15

  c = 3x +2 = 3(11) +2 = 35

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Comment on problem 8

You will notice that the side lengths do not satisfy the triangle inequality: the sum of the short sides is not greater than the long side. These side lengths cannot form a triangle. Cute algebra, but bad geometry.