Mathematics

Question

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1 Answer

  • first we find width or legnth,
    then we determine which wire is shortest
    a wire=264

    legnth used for rectangle=x

    legnth used for square=264-x=y

    reactangle=2legnh+2width=2(l+w)
    l=2w-4
    subsitute
    2(2w-4+w)=recangle perimiter=4w-8+2w=6w-8



    square=y
    legnth=width
    legnth=rectangleleghtn+width (rectangle l+w=3w-4)
    4legnth=perimiter=12w-16


    recangle perimiter=6w-8
    square perimiter=12w-16
    x+y=264
    (6w-8)+(12w-16)=legnth of wire toatl
    18w-24=total widght=264
    18w-24=264
    add 24 to both sides
    18w=288
    divide both sides by 18
    w=16
    perimter of square=4(l+w)
    l=2w-4
    l=2(16)-4
    l=28
    perimiter of square 4(28+16)=4(44)=176
    176=y
    x+y=264
    x+176=264
    subtract 176 from both sides
    x=88
    rectangle=88
    88<176

    rectangle is shorter wire which is 88 cm in total legnth

    88cm is answer