Question

The perimeter of an isosceles triangle is 4 times the length of the shortest side. The longer sides are 4.5 ft longer than the shortest side. What is the length of each side of the triangle?​

Answer 1

• Shorter side = 9 feet
• Longer sides = 13.5 feet

Explanation:

Let :

• Shorter side = x
• Longer sides = x + 4.5
• Perimeter = 4x

Solving

• 2(x + 4.5) + x = 4x
• 2x + 9 + x = 4x
• x = 9 feet

Solution

• Shorter side = 9 feet
• Longer sides = 13.5 feet

Answer 2

• short side: 9 ft
• longer sides: 13.5 ft

Explanation:

The given information lets us write two equations relating the side lengths.

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setup

Let L and S represent the lengths of the longer and shorter sides. We are told ...

S + L + L = 4S . . . . . the perimeter is 4 times the short side length

L = 4.5 +S

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solution

Using the second equation to substitute for L in the first equation, we have ...

S +2(4.5 +S) = 4S

9 = S . . . . . . . . . . . . . simplify, subtract 3S

L = 4.5 +S = 13.5

The shortest side is 9 ft; the longer sides are 13.5 ft.

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Additional comment

The perimeter is 36 ft.