A triangle has side lengths of left bracket, 8, f, plus, g, right bracket(8f+g) centimeters, left bracket, 4, f, minus, 5, h, right bracket(4f−5h) centimeters, and left bracket, 9, h, plus, 7, g, right bracket(9h+7g) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
The perimeter of a triangle is the sum of the lengths of its three sides.
Therefore, the expression that represents the perimeter of the triangle is:
(8f + g) + (4f - 5h) + (9h + 7g)
The perimeter of a triangle is the sum of its three side lengths. Using the given expressions for the side lengths of the triangle, the perimeter can be represented as:
Perimeter = (8f+g) + (4f-5h) + (9h+7g)
Simplifying the expression, we get:
Perimeter = 8f + g + 4f - 5h + 9h + 7g
Combining like terms, we have:
Perimeter = (8f + 4f) + (g + 7g) + (-5h + 9h)
Simplifying further, we get:
Perimeter = 12f + 8g + 4h
Therefore, the expression that represents the perimeter of the triangle is 12f + 8g + 4h centimeters.
To find the perimeter of a triangle, we need to sum up the lengths of all three sides.
The given lengths of the sides of the triangle are:
Side 1: (8f + g) cm
Side 2: (4f - 5h) cm
Side 3: (9h + 7g) cm
To find the perimeter, we add up these three sides:
Perimeter = Side 1 + Side 2 + Side 3
= (8f + g) + (4f - 5h) + (9h + 7g)
= 8f + g + 4f - 5h + 9h + 7g
Combining the like terms, we get:
Perimeter = (8f + 4f + 7g) + (9h - 5h) + g
= 12f + 7g + 4h
Therefore, the expression that represents the perimeter of the triangle is:
12f + 7g + 4h centimeters.