1/2 × diagonal × sum of offsets = Area of
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Let the area of quadrilateral ABCD = 468.75 sq cm.
Let the AD be the diagonal on which the altitude BP = 3x and CQ = 2x.
AD = 1.5(3x+2x) = 7.5x.
Area of triangle ABD = 7.5x*3x/2 = 468.75*3/5, or
22.5x^2 = 2*468.75*3/5 = 187.5
x^2 = 187.5/22.5 = 25
x = 5
Hence AD = 5*7.5 = 37.5 cm.
BP = 3*5 = 25 cm
CQ = 2*5 = 20 cm
Let the AD be the diagonal on which the altitude BP = 3x and CQ = 2x.
AD = 1.5(3x+2x) = 7.5x.
Area of triangle ABD = 7.5x*3x/2 = 468.75*3/5, or
22.5x^2 = 2*468.75*3/5 = 187.5
x^2 = 187.5/22.5 = 25
x = 5
Hence AD = 5*7.5 = 37.5 cm.
BP = 3*5 = 25 cm
CQ = 2*5 = 20 cm
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