A rectangle is made up of the equations; For the longer spans: 5x-12y+16 and 5y-4x+20; for the shorter spans: 2x-4y+4 and 3x-2y-12
Initially solve for the longer spans through simultaneous equations;5x-12y+16=5y-4x+20Simplify equation;9x-17y-4=0Repeat for the shorter spans;2x-4y+4=3x-2y-12Simplify equation;x+2y-16=0Make x the subject;x=16-2ySubstitute value for x into the first found equation;9(16-2y)-17y-4=0Expand brackets and simplify;144-18y-17y-4=0140-35y=0Solve to find y;35y=140y=4Substitute y value back into equation to find x value;x=16-2(4)Expand brackets and solve;x=16-8x=8Substitute values for x and y into span length equations to find the spans;Shorter span: 2(8)-4(4)+4=4Longer span: 5(4)-4(8)+20=8Therefore the rectangle dimensions are 8 by 4 (same as x and y values)
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