Question

what is the largest perimeter of an isosceles triangle with side lengths of 30 and 40? your answer

Explanation:

Step1: Consider two cases for the isosceles triangle

Case 1: The equal sides (legs) are \(30\). Then the sides are \(30,30,40\).
Case 2: The equal sides (legs) are \(40\). Then the sides are \(40,40,30\).

Step2: Check the triangle - inequality theorem for both cases

For a triangle with side lengths \(a,b,c\), the triangle - inequality theorem states that \(a + b>c\), \(a + c>b\), and \(b + c>a\).

• Case 1:
• \(30+30 = 60>40\)
• \(30 + 40=70>30\)
• \(30+40 = 70>30\)

The perimeter \(P_1=30 + 30+40=100\).

• Case 2:
• \(40+40=80>30\)
• \(40 + 30=70>40\)
• \(40+30=70>40\)

The perimeter \(P_2=40 + 40+30=110\).

Answer:

\(110\)