Pablo folds a straw into a triangle with side lengths of 4x2−3 inches, 4x2−2 inches, and 4x2−1 inches. Which expression can be used to find the perimeter of the triangle, and what is the perimeter when x = 1.5? 12x2 −6; 21 inches
12x2; 27 inches
12x2 −6; 30 inches
12x2; 36 inches

12x² - 6; 21 inches ⇒ A

Step-by-step explanation:

Let us solve the question

∵ The side lengths of a triangle are 4x² - 3 in., 4x² - 2 in., 4x² - 1 in.

∴ S1 = 4x² - 3 inches

∴ S2 = 4x² - 2 inches

∴ S3 = 4x² - 1 inches

→ The perimeter of the triangle is the sum of the lengths of its 3 sides

∵ P = S1 + S2 + S3

∴ P = 4x² - 3 + 4x² - 2 + 4x² - 1

→ Add the like terms

∵ P = (4x² + 4x² + 4x²) + (-3 + -2 + -1)

∴ P = 12x² + -6

→ Remember (+)(-) = (-)

∴ P = 12x² - 6

∴ The expression of the perimeter of the Δ is 12x² - 6

∵ x = 1.5

→ Substitute x in the perimeter expression by 1.5

∵ P = 12(1.5)² - 6

∴ P = 12(2.25) - 6

∴ P = 27 - 6

∴ P = 21 inches

∴ The perimeter of the triangle is 21 inches

The expression can be used to find the perimeter of the triangle is 12x² - 6 and its perimeter is 21 inches when x = 1.5

1,918

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