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college algebra

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if the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. if the altitude is increased by 3 inches and the base is decreased by 2 inches the area will be increased by 5 square inches. find the base and the altitude of the triangle.

  • college algebra - ,

    let original base be b and height be h

    original area = bh/2

    case1:
    new base = b+4
    new height = h+4
    new area = (b+4)(h+4)/2 = bh/2 + 42
    bh + 4b + 4h + 16 = bh + 84
    4b + 4h = 68
    b+h = 17 #1

    case2:
    new base = b-2
    new height = h+3
    new area = (b-2)(h+3)/2 = bh/2 + 5
    bh + 3b - 2h - 6 = bh + 10
    3b - 2h = 16 #2

    #1 x 2 ---->2b+2h= 34
    add to #2
    5b = 50
    b = 10
    a = 7

    original base is 10 inches
    original height is 7 inches

    check:
    original area = 35
    case1:
    area = 14(11)/2 = 77 , it increased by 42
    case2:
    area = (10)(8)/2 = 40 , it increased by 5

    all is good!

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