Question

a triangle has side lengths of $(6.2g + 3.4)$ centimeters, $(1.9g - 5.3)$ centimeters, and $(9.3h + 1.2)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$10.5h + 6.2g$
$-1.9 + 10.5h + 8.1g$
$-3.4 + 9.6g + 10.5h$
$-0.7 + 9.3h + 8.1g$
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Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So, \(P=(6.2g + 3.4)+(1.9g-5.3)+(9.3h + 1.2)\).

Step2: Remove the parentheses

Using the associative property of addition \(a+(b + c)=(a + b)+c\), we get \(P = 6.2g+3.4 + 1.9g-5.3+9.3h + 1.2\).

Step3: Group like - terms

Group the \(g\) - terms, \(h\) - terms and constant terms: \((6.2g+1.9g)+9.3h+(3.4 - 5.3+1.2)\).

Step4: Combine like - terms

For the \(g\) - terms: \(6.2g+1.9g=(6.2 + 1.9)g=8.1g\).
For the constant terms: \(3.4-5.3 + 1.2=(3.4+1.2)-5.3=4.6-5.3=-0.7\).
The \(h\) - term remains \(9.3h\).

Answer:

\(-0.7 + 9.3h+8.1g\)