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Given parallelogram EFGH, where EF = 2x+15, HE = 6x+4 and the perimeter is 69, which is the value of GH?

User Deejayy
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1 Answer

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Answer: The perimeter of a parallelogram is the sum of the lengths of all four sides. In this case, the perimeter is given as 69, so we can write:

EF + FG + GH + HE = 69

We know that opposite sides of a parallelogram are equal in length, so EF = GH and FG = HE. Substituting these into the equation above, we get:

2(EF) + 2(FG) = 69

2(GH) + 2(HE) = 69

Simplifying each equation:

2(2x+15) + 2(6x+4) = 69

4x + 30 + 12x + 8 = 69

16x + 38 = 69

16x = 31

x = 31/16

Substituting x into the equation for GH, we get:

GH = 2x+15

GH = 2(31/16) + 15

GH = 31/8 + 120/8

GH = 151/8

Therefore, the value of GH is 18.875 units.

Explanation:

User Mesocyclone
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