Question

A triangle has side lengths of (4.5x + 7.5y)cm, (8.4x +2.5z) cm, and (1.5z - 4.5y) cm. Which expression represents the perimeter, in centimeters, of the triangle?

1) 19.9xyz
2) 12xy + - 3yz
3) 12.9x + 3y + 4z
4) 12.9x - 12y + 4z

Answer 1

The expression for the perimeter of the triangle is 12.9x + 3y + 4z cm, found by summing the like terms of the triangle's three given side lengths.

Step-by-step explanation:

To find the perimeter of a triangle, you simply add the lengths of all three sides together. Given the side lengths are (4.5x + 7.5y) cm, (8.4x +2.5z) cm, and (1.5z - 4.5y) cm, you can combine like terms in this addition.

Perimeter = (4.5x + 7.5y) + (8.4x +2.5z) + (1.5z - 4.5y)

Combine the x terms: 4.5x + 8.4x = 12.9x

Combine the y terms: 7.5y - 4.5y = 3y

Combine the z terms: 2.5z + 1.5z = 4z

Adding these together gives the total perimeter:

Perimeter = 12.9x + 3y + 4z

Therefore, the expression representing the perimeter in centimeters of the triangle is 12.9x + 3y + 4z, which corresponds to option 3).