Answer:
From largest to smallest: FG, FH, GH
Step-by-step explanation:
Given
[tex]FG = 6x + 7[/tex]
[tex]GH = 8x - 5[/tex]
[tex]FH = 10x - 11[/tex]
[tex]Perimeter = 87[/tex]
Required
Order the sides in descending order
First, we need to solve for x.
Perimeter of FGH is calculated as thus:
[tex]Perimeter = FG + GH + FH[/tex]
Substitute values for FG, GH, FH and Perimeter
[tex]87 = 6x + 7 + 8x - 5 + 10x - 11[/tex]
Collect Like Terms
[tex]87 - 7 + 5 + 11= 6x + 8x + 10x[/tex]
[tex]96= 24x[/tex]
Reorder
[tex]24x = 96[/tex]
Divide through by 24
[tex]x = 96/24[/tex]
[tex]x = 4[/tex]
Substitute 4 for x in FG, GH and FH
[tex]FG = 6x + 7[/tex]
[tex]FG = 6 * 4 + 7[/tex]
[tex]FG = 24 + 7[/tex]
[tex]FG =31[/tex]
[tex]GH = 8x - 5[/tex]
[tex]GH = 8 * 4 - 5[/tex]
[tex]GH = 32 - 5[/tex]
[tex]GH = 27[/tex]
[tex]FH = 10x - 11[/tex]
[tex]FH = 10*4 - 11[/tex]
[tex]FH = 40 - 11[/tex]
[tex]FH = 29[/tex]
In order of arrangement in descending order, we have:
[tex]FG =31[/tex] [tex]FH = 29[/tex] [tex]GH = 27[/tex]
