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An architect is designing a small A-frame cottage for a new resort area. A cross section of the cottage is an isosceles triangle with an area of 98 square feet. The front wall of the cottage must a accommodate a sliding door that is 6 feet wide and 8 feet high. Find the width and height of the cross section

  • math/geometry -

    center the door way so that half the base is 3+x feet. The area of the triangle is 98, so the height h = 98/(3+x)

    using similar triangles,

    8/x = h/(x+3)
    8(x+3) = hx
    8(x+3) = 98/(x+3) * x
    4x^2 - 25x + 36 = 0
    (4x-9)(x-4) = 0

    Looks like any x from 9/4 to 4 will work. So, the dimensions can vary from

    10.5 ft wide x 18 2/3 ft high
    14 wide x 16 ft high

  • math/geometry -


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