ABCD is a square and P,Q are the midpoints of BC,CD respectively.If AP=a and AQ=b,
a = b
let x be the side of the square
△ADQ:\vartriangle ADQ:△ADQ:
AD = x; DQ = x2\dfrac{x}{2}2x; AQ = b = a
by the Pythagorean theorem:
x2+x24=a2=b2x^2 + \dfrac{x^2}{4} = a^2 = b^2x2+4x2=a2=b2
4x2+x2=4a2=4b24x^2 + x^2 = 4a^2 = 4b^24x2+x2=4a2=4b2
5x2=4a2=>x2=4a25=4b255x^2 = 4a^2 => x^2 = \dfrac{4a^2}{5} = \dfrac{4b^2}{5}5x2=4a2=>x2=54a2=54b2 - area of a square ABCD
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