Question

an equilateral triangle is a triangle where all three sides have the same length. complete the table to show the side lengths and perimeters for several equilateral triangles. side length perimeter 3 10 81 315

Explanation:

Step1: Recall the formula for the perimeter of an equilateral triangle

The perimeter \(P\) of an equilateral triangle with side length \(s\) is \(P = 3s\).

Step2: Calculate the perimeter when \(s = 3\)

Substitute \(s = 3\) into \(P=3s\).
\(P = 3\times3=9\)

Step3: Calculate the perimeter when \(s = 10\)

Substitute \(s = 10\) into \(P = 3s\).
\(P=3\times10 = 30\)

Step4: Calculate the side length when \(P = 81\)

Use the formula \(s=\frac{P}{3}\). Substitute \(P = 81\) into \(s=\frac{P}{3}\).
\(s=\frac{81}{3}=27\)

Step5: Calculate the side length when \(P = 315\)

Use the formula \(s=\frac{P}{3}\). Substitute \(P = 315\) into \(s=\frac{P}{3}\).
\(s=\frac{315}{3}=105\)

Answer:

Side Length	Perimeter
\(10\)	\(30\)
\(27\)	\(81\)
\(105\)	\(315\)