Question #160239

ABCD is a square and P,Q are the midpoints of BC,CD respectively.If AP=a and AQ=b,


1
Expert's answer
2021-02-02T03:39:39-0500


a = b


let x be the side of the square


ADQ:\vartriangle ADQ:

AD = x; DQ = x2\dfrac{x}{2}; AQ = b = a


by the Pythagorean theorem:


x2+x24=a2=b2x^2 + \dfrac{x^2}{4} = a^2 = b^2

4x2+x2=4a2=4b24x^2 + x^2 = 4a^2 = 4b^2

5x2=4a2=>x2=4a25=4b255x^2 = 4a^2 => x^2 = \dfrac{4a^2}{5} = \dfrac{4b^2}{5} - area of a square ABCD



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