Question

Find the measure of x, each side of triangle FGH, and then classify the triangle as equilateral, isosceles, or scalene. FG = 3x + 10, GH = 5x - 8, FH = 4x + 1. The perimeter of the triangle is 111 ft.

A) x=8,FG=34,GH=32,FH=33,Isosceles
B) x=7,FG=31,GH=29,FH=32,Equilateral
C) x=9,FG=37,GH=35,FH=36,Scalene
D) x=8,FG=34,GH=32,FH=33,Scalene

Answer 1

After solving the perimeter equation for x and finding it to be 9, we substitute it back into the expressions to find that FG = GH = FH = 37 ft, revealing that triangle FGH is an equilateral triangle.

Step-by-step explanation:

To find the value of x and classify the triangle FGH, we use the given expression for each side and the perimeter.

Perimeter of triangle FGH = FG + GH + FH = 111 ft.

Substituting the expressions:

3x + 10 + 5x - 8 + 4x + 1 = 111

Combining like terms:

12x + 3 = 111

Subtract 3 from both sides:

12x = 108

Divide by 12:

x = 9

Now we substitute x = 9 into the expressions:

FG = 3(9) + 10 = 37

GH = 5(9) - 8 = 37

FH = 4(9) + 1 = 37

Since all sides are equal, the triangle is equilateral.

Thus, the correct answer is:

x = 9, FG = 37 ft, GH = 37 ft, FH = 37 ft, and the triangle is equilateral.