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An isosceles triangle and a rectangle share a base. The area of the rectangle is 4 times the area of the triangle. The area of the triangle is 60 cm^2 and its height is 15 cm. Find the dimensions of the triangle.

  • Math -

    Triangle Area = 1/2 bh

    60 = 1/2 15b
    120 = 15b
    b = 8

    base = 8
    height = 15
    s = sides
    The height h of the isosceles triangle
    h = (sqrt(s^2 - 1/4 b^2))
    15 = (sqrt(s^2 - 1/4 8^2))
    15 = (sqrt(s^2 - 1/4 64))
    15 = (sqrt(s^2 - 16))
    Square both sides
    225 = s^2 - 16
    s^2 = 241
    s = 15.52

    Or, you can use the Pythagorean theorem
    The height forms two right triangles.
    side a = 15
    side b = 4 (8/2 = 4)
    side c = hypotenuse (side of isosceles)

    c^2 = 4^2 + 15^
    c^2 = 16 + 225
    c^2 = 241
    c = 15.52

    Dimensions of triangle,
    Equal sides = 15.52
    base = 8

  • Math -

    The ratio between the area and the perimeter of a rectangular sheet of paper is 7:5.if the area of the sheet is 38.5cm² find its perimeter

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