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1 December, 01:52

triangle STU is an equilateral triangle. If ST is one less than twice x, SU is 37 less than five times x, and TU is 11 more than x, find x and the measure of each.

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  1. 1 December, 02:50
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    The value of x = 12 and the measure of each side is 23 units.

    Step-by-step explanation:

    Given: STU is an equilateral triangle.

    ST = 2x - 1

    SU = 5x - 37

    TU = x + 11

    Now, as Δ STU is an equilateral triangle, hence all the sides of the triangle are equal.

    ⇒ ST = SU = TU

    or, 2x - 1 = 5x - 37 = x + 11

    Considering : 2x - 1 = 5x - 37, we get

    -1 + 37 = 5x - 2x

    or 3x = 36

    or, x = 12

    Considering : 5x - 37 = x + 11, we get

    5x - x = 11 + 37

    or, 4x = 48 or, x = 12

    Considering : x + 11 = 2x - 1

    or, 2x - 1 = x + 11

    or, x = 12

    hence, in all the cases value of x = 12

    ST = 2x - 1 = 2 (12) - 1 = 23 units

    SU = 5x - 37 = 5 (12) - 1 = 23 units

    TU = x + 11 = 12 = 11 = 23 units
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