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A triangle has side lengths of
(5.1 g-6.9 h) centimeters,
(6.4 g-8.8 k) centimeters, and
(9.3 k+3.4 h) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

-3.5 h+0.5 k+11.5 g

-1.8 gh-2.4 gk+12.7 hk

-12.3 hk+20.8 gk

-5.4 k+11.5 g+2.4 h

A triangle has side lengths of $(5.1 g-6.9 h)$ centimeters, $(6.4 g-8.8 k)$ centimeters, and $(9.3 k+3.4 h)$ centimeters. Which expression represents the perimeter, in centimeters, of the triangle? $\newline$ $-3.5 h+0.5 k+11.5 g$ $\newline$ $-1.8 g h-2.4 g k+12.7 h k$ $\newline$ $-12.3 h k+20.8 g k$ $\newline$ $-5.4 k+11.5 g+2.4 h$

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Convert equations of conic sections from general to standard form

Full solution

Q. A triangle has side lengths of

(5.1 g-6.9 h)

centimeters,

(6.4 g-8.8 k)

centimeters, and

(9.3 k+3.4 h)

centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

\newline

-3.5 h+0.5 k+11.5 g

\newline

-1.8 g h-2.4 g k+12.7 h k

\newline

-12.3 h k+20.8 g k

\newline

-5.4 k+11.5 g+2.4 h

Calculate Perimeter: To find the perimeter of the triangle, we need to add the lengths of all three sides together. The perimeter $P$ is given by the formula: $\newline$ $P = \text{side1} + \text{side2} + \text{side3}$ $\newline$ So, we will add the expressions for each side: $\newline$ $(5.1 g - 6.9 h) + (6.4 g - 8.8 k) + (9.3 k + 3.4 h)$
Combine Like Terms: Now, we combine like terms. We will add the coefficients of $g$ , subtract the coefficients of $h$ , and add the coefficients of $k$ : $\newline$ For $g$ : $5.1 + 6.4 = 11.5$ $\newline$ For $h$ : $-6.9 + 3.4 = -3.5$ $\newline$ For $k$ : $-8.8 + 9.3 = 0.5$ $\newline$ So, the combined expression is: $\newline$ $11.5 g - 3.5 h + 0.5 k$
Check Math: We check the math to ensure there are no errors in the calculation. The coefficients have been correctly added and subtracted according to their respective variables.

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