Question

perimeter less than or equal to 60, because it c is close to 34 then p=14+20+33=67<60 if tess wants the third side of the garden to have an integer length, what is the smallest amount of fencing she would need? (with a triangle image labeled with sides 14 ft, 20 ft, and vertices b, c)

Explanation:

Step1: Apply triangle - side - length relationship

The triangle - side - length relationship states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 14\) and \(b=20\). So \(|20 - 14|\lt c\lt20 + 14\), which simplifies to \(6\lt c\lt34\).

Step2: Find the smallest integer value of \(c\)

Since \(c\) is an integer and \(6\lt c\), the smallest integer value of \(c\) is \(7\).

Step3: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b + c\). Substituting \(a = 14\), \(b = 20\), and \(c = 7\) into the formula, we get \(P=14+20 + 7\).

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Answer:

\(41\) ft