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Squares inscribed in right triangle

Source: LIMIT 2020 Cat 1 Obj P18

May 2, 2020
geometrylimit

Problem Statement

Let △ABC\triangle ABC be a right triangle with ∠C=90∘\angle C=90^{\circ}. Two squares S1S_1 and S2S_2 are inscribed in the triangle ABCABC such that S1S_1 and ABCABC share a common vertex CC and S2S_2 has one of its sides on ABAB. Suppose that Area(S1)=1+Area(S2)=441\text{Area}(S_1)=1+\text{Area}(S_2)=441, then calculate AC+BCAC+BC
(A)400400 (B)420420 (C)441441 (D)462462
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