percent of the area problem. help plz!!!?

A cow is bound at the center if a rectangular field measuring 12 feet * 24feet . If the rope with which the cow is tied is 10 feet long, approx. what percent of the area of the field can the cow graze upon?

thanks in advance

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  • 8 years ago
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    Jaher Wasim Hi!

    Percent of the area problem. help plz!!!?

    A cow is bound at the center if a rectangular field measuring 12 feet * 24feet . If the rope with which the cow is tied is 10 feet long, approx. what percent of the area of the field can the cow graze upon?

    thanks in advance

    Your problem look simple but not as simple as it is solved than seen . It catches my interest.

    I hope you are still here ti witness.

    Area of the field = 12 x 24

    Area of the field = 288 ft²

    Refer to Figure: http://www.flickr.com/photos/27678773@N06/81909279...

    Sin EOb = bE / Ob

    Sin EOb = 12/2 /10

    Sin EOb = 0.6 Ft

    ∢EOb = 36.87°

    Cos EOb = OE / Ob

    OE = Ob Cos EOb

    OE = 10 (0.8)

    OE = 8 Ft

    EF = OE x 2

    EF = 16 Ft

    Area Sector ArcabOa = 1/2R²(EQb x 2)

    Area Sector ArcabOa = ½(10)²(36.87 x 2) x π/180

    Area Sector ArcabOa = 64.35 ft²

    At the Opposite Side

    Area Sector ArcabOa = Area Sector ArccdOc = 64.35 ft²

    Area Δ aOG = 1/2aG(OG)

    Note → aG = OE = 8 ← refer to figure

    note → OG = Ea = bE = 12/2 ← refer to figure

    Area Δ aOG = ½(8)(6)

    Area Δ aOG = 24 ft²

    Area Δ aOG = Area Δ dOG = 24 Ft²

    Area Δ aOd = Area Δ aOG + Area Δ dOG

    Area Δ aOd = 24 + 24

    Area Δ aOd = 48 ft²

    The Oppodite Side Area Δ bOc = Area Δ aOd = 48 ft²

    Graze Land Area = Area Sector ArcabOa + Area Sector ArcccOc + Area Δ aOd + Area Δ bOc

    Graze Land Area = 64.35 + 64.35 + 48 + 48

    Graze Land Area = 224.7 ft²

    The Percentage of Grazing Area = 224.7 / 288

    =============================================

    The Percentage of Grazing Area = 78.02 % ◄ Ans

    =============================================

    Hope this helps

    Remember that Jesus loves you. Know Him in His words the Bible.

    God Bless

    Lim♥E

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