Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
28th May, 2025

Let single side of the square be x.


Notice;


PB=¼(AB)=¼(x).


Calculating single side length of square ABCD.


It will be;


Area triangle ADP of height x and base (x-¼(x)) + area triangle DOP of base (√(x²+(x-¼(x))²)) and height 4 unit + 2(area triangle DOC of height 4 unit and base x) + area triangle OPB of height (x-4) and base ½(x) = area square ABCD with length and width x respectively.


Therefore;


½(x*(3x/4))+½(4√(x²+(3x/4)²)+½(8x)+½(¼(x)(x-4))=x²


(3x²)/8+2√(x²+(9x²/16))+4x+(x²/8)-(x/2)=x²


3x²+16√(x²+(9x²/16))+32x+x²-4x=8x²


16√(x²+(9x²/16))=4x²-28x


256(x²+(9x²/16))=(4x²-28x)²


256x²+144x²=16x⁴-228x³+784x²


16x⁴-228x³+784x²-400x²=0


16x⁴-228x³+384x²=0


x²-14x+24=0


x²-12x-2x+24=0


x(x-12)-2(x-12)=0


(x-2)(x-12)=0


Therefore;


x≠2


x=12.


Therefore single side of the square ABCD is;


12 units.

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