Question

The perimeter of a triangle shown is 20 inches write an expression for the perimeter then write an equation that you can use to find the length of each side

Answer 1

A + B + C = 20 in

A² = B² + C² - 2·B·C·cos(α)

B² = C² + A² - 2·A·C·cos(β)

C² = A² + B² - 2·A·B·cos(γ)

Explanation:

The expression for the perimeter of a triangle with sides A, B, C is

Perimeter of triangle = A + B + C = 20 inches

A² = B² + C² - 2·B·C·cos(α)

B² = C² + A² - 2·A·C·cos(β)

C² = A² + B² - 2·A·B·cos(γ)

Where, angle α is the angle opposite of side A

angle β is the angle opposite of side B

angle γ is the angle opposite of side C.

Answer 2

Assuming the triangle is an equilateral triangle (all sides and angles are equal), the equation 3x = 20 would be used to find the length of each side.

Explanation:

Formula for perimeter of triangle:

P = a + b + c

where a, b and c are the sides of the triangle.

Assuming the triangle is equilateral, all sides would be equal,

a = b = c = x

⇒ P = x + x + x

∴ 20 = 3x.