a triangle has a base area of (2 -x) cm and a height of (2x+6) cm.?

What is the maximum area of the triangle. What value of x will produce the maximum area?

Update:

PLEASE HELP

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  • ted s
    Lv 7
    7 months ago

    Hmmmm....base area in cm.....what does that mean ???

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  • 7 months ago

    A = (0.5)(2-x)(2x + 6)

    2A = 4x + 12 - 2x^2 - 6x

    2A = -2x^2 - 2x + 12

    A = -x^2 - x + 6

    At Max (Area)

    dA/dx = -2x - 2 = 0

    2x = -2

    x = -1

    Hence

    A = (0.5)(2 -- - 1)(2(-1) + 6)

    A = ).5)(3)(4)

    A = (0.5)(12)

    A = 6 (Max Area) at x = -1

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