Question

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

Answer 1

From largest to smallest: FG, FH, GH

Explanation:

Given

`FG = 6x + 7`

`GH = 8x - 5`

`FH = 10x - 11`

`Perimeter = 87`

Required

Order the sides in descending order

First, we need to solve for x.

Perimeter of FGH is calculated as thus:

`Perimeter = FG + GH + FH`

Substitute values for FG, GH, FH and Perimeter

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

Collect Like Terms

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

`96= 24x`

Reorder

`24x = 96`

Divide through by 24

`x = 96/24`

`x = 4`

Substitute 4 for x in FG, GH and FH

`FG = 6x + 7`

`FG = 6 * 4 + 7`

`FG = 24 + 7`

`FG =31`

`GH = 8x - 5`

`GH = 8 * 4 - 5`

`GH = 32 - 5`

`GH = 27`

`FH = 10x - 11`

`FH = 10*4 - 11`

`FH = 40 - 11`

`FH = 29`

In order of arrangement in descending order, we have:

`FG =31`
`FH = 29`
`GH = 27`