Question

An obtuse triangle has side lengths of (5.5x + 6.2y) centimeters, (4.3x + 8.3z )and (1.6z + 5.1y) centimeters. Which expression represents the perimeter, in centimeters of the obtuse triangle? PLZ HELP ASAP :)

Answer 1

The expression
`9.8x+11.3y+9.9z` represents the perimeter, in centimeters of the obtuse triangle.

Explanation:

An obtuse triangle is a triangle where one of the internal angles is obtuse (greater than 90 degrees).

The perimeter of a triangle is the total distance around the outside of a triangle, which can be found by adding together the length of each side. Or as a formula:

`P=a+b+c`

where:

a, b and c are the lengths of each side of the triangle.

We know that the triangle has side lengths of
`a = 5.5x + 6.2y`,
`b= 4.3x + 8.3z` and
`c=1.6z + 5.1y` centimeters. Therefore, the perimeter is

`P=a+b+c\\P=(5.5x + 6.2y)+(4.3x + 8.3z)+(1.6z + 5.1y)\\\\\mathrm{Group\:like\:terms}\\P=5.5x+4.3x+6.2y+5.1y+8.3z+1.6z\\\\\mathrm{Add\:similar\:elements:}\\P=9.8x+11.3y+9.9z`