Question

Triangle FGH has the following information Perimeter of triangle - 87 Segment FG (6x + 7) Segment GH (8x - 5) Segment FH (10x - 11) Solve for x. Solve for the length of each side. Solve for the perimeter

Answer 1

Therefore, the length of each side of triangle FGH is 31, 27, and 29, and the perimeter is 87.

Explanation:

To solve for the length of each side and the perimeter of triangle FGH, follow these steps:

Step 1: Set up the equation for the perimeter

The perimeter of a triangle is the sum of the lengths of its sides. So, we can set up the equation:

Perimeter = FG + GH + FH

Step 2: Substitute the expressions for the side lengths

We are given that FG = 6x + 7, GH = 8x - 5, and FH = 10x - 11. Substituting these expressions into the perimeter equation, we get:

Perimeter = (6x + 7) + (8x - 5) + (10x - 11)

Step 3: Combine like terms

Combining like terms, we get:

Perimeter = 24x - 9

Step 4: Set the perimeter equal to 87 and solve for x

We are given that the perimeter of triangle FGH is 87. Setting the perimeter equation equal to 87 and solving for x, we get:

24x - 9 = 87

24x = 96

x = 4

Step 5: Calculate the length of each side

Now that we know the value of x, we can calculate the length of each side:

FG = 6x + 7 = 6(4) + 7 = 24 + 7 = 31

GH = 8x - 5 = 8(4) - 5 = 32 - 5 = 27

FH = 10x - 11 = 10(4) - 11 = 40 - 11 = 29

Step 6: Calculate the perimeter

Now that we have the lengths of all three sides, we can calculate the perimeter:

Perimeter = FG + GH + FH = 31 + 27 + 29 = 87