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11 April, 08:45

The perimeter of an equilateral triangle is 6 inches more than the perimeter of a square, and the side of the triangle is 4 inches longer than the side of the square. Find the side of the triangle

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  1. 11 April, 08:55
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    The length of the side of the triangle is 10 inches.

    Step-by-step explanation:

    Let p = perimeter of the equilateral triangle

    Let P = perimeter of the square

    Let s = length of side of the triangle

    Let S = length of side of the square

    "The perimeter of an equilateral triangle is 6 inches more than the perimeter of a square"

    p = P + 6 Equation 1

    "the side of the triangle is 4 inches longer than the side of the square"

    s = S + 4 Equation 2

    We have 2 equations and 4 unknowns. We need two more equations. We use the definition of perimeter to get the other two equations.

    For an equilateral triangle,

    p = 3s Equation 3

    For a square,

    P = 4S Equation 4

    Substitute p and P of Equation 1 with equations 3 and 4. Then write equation 2.

    3s + 4S = 6

    s = S + 4

    Now we have a system of 2 equations in 2 unknowns. We can solve for s and S. We can use the substitution method. Solve the second equation for S.

    S = 4 - s

    Substitute S = 4 - s into equation 3s + 4S = 6.

    3s + 4 (4 - s) = 6

    3s + 16 - 4s = 6

    -s = - 10

    s = 10

    Answer: The length of the side of the triangle is 10 inches.
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