The sides of AFGH are FG = 6x+7, GH = 8x - 5, and FH = 10x - 11. If the perimeter of FGH is 87, list the angles in order from largest to smallest.

Based on the relationship of angles and sides of a triangle, the angles from the largest to the smallest are: ∠H,  ∠G, ∠F

Recall:

Given ΔFGH with the following sides:

FG = 6x+7 (opposite to ∠H)

GH = 8x - 5 (opposite to ∠F)

FH = 10x - 11 (opposite to ∠G)

Perimeter of ΔFGH = 87

Find the value of x using the perimeter formula to create an equation.

Thus:

FG + GH + FH = 87

6x + 7 + 8x - 5 + 10x - 11 = 87

24x - 9 = 87

24x = 87 + 9

24x = 96

x = 4

Plug in the value of x to find the length of each side:

FG = 6x+7 = 6(4) + 7 = 31 (opposite to ∠H)

GH = 8x - 5 = 8(4) - 5 = 27 (opposite to ∠F)

FH = 10x - 11 = 10(4) - 11 = 29 (opposite to ∠G)

Therefore, based on the relationship of angles and sides, the angles from the largest to the smallest are: ∠H,  ∠G, ∠F

Learn more about relationship of angles and sides of a triangle on:

link

∠ H, ∠G, ∠F

Step-by-step explanation:

6x + 7 + 8x - 5 + 10x - 11 = 87

24x = 96

x = 96 / 24 = 4

FG = 6(4) + 7 = 31 units

GH = 8(4) - 5 = 27 units

FH = 10(4) - 11 = 29 units

FG is the longest side ⇒ ∠H is the largest angle.

GH is the shortest side ⇒ ∠F is the smallest angle

∠ H, ∠G, ∠F

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