I think the dimensions of the rectangle are sqr(2a^2) and sqr(2b^2) if two ticks are b and one tick is a. IDK where to continue though
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shaded area = $a^2+b^2 = 50 \, cm^2$ $|MK| = \sqrt{(a\sqrt{2})^2 + (b\sqrt{2})^2}$