A Quadrilateral ABCD in which AD= 13 cm ,DC = 12 cm , BC = 3 cm and angle ABD = angle BCD = 90 DEGREE . Calculate the length  of AB

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{In} \mathrm{right}-\mathrm{angled} \mathrm{triangle} BCD, \\ BD=\sqrt{B{C}^2+C{D}^2} \\ =\sqrt{3^2+{12}^2} \\ =\sqrt{9+144} \\ =\sqrt{153} \mathrm{cm} \\ \mathrm{In} \mathrm{right}-\mathrm{angled} \mathrm{triangle} ABD, \\ AB=\sqrt{A{D}^2-B{D}^2} \\ =\sqrt{{13}^2-{\left(\sqrt{153}\right)}^2} \\ =\sqrt{169-153} \\ =\sqrt{16} \mathrm{cm} \\ =4 \mathrm{cm} \end{gathered}$$

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