Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms

Option A[tex]\frac{12}{36} = \frac{13}{39} = \frac{1}{3}[/tex] is the the ratio of corresponding sides for the similar trianglesSolution:We have to write the ratio of corresponding sides for the similar trianglesWhen two figures are similar, the ratios of the lengths of their corresponding sides are equal.The given figure in question is attached below with sides marked as ABC for bigger triangle and XYZ for smaller triangleTherefore,[tex]\frac{XY}{AC} = \frac{YZ}{CB}[/tex]In the attached figure,XY = 12AC = 36YZ = 13CB = 39Substituting these we get,[tex]\frac{12}{36} = \frac{13}{39}[/tex]Reducing to lowest terms we get,[tex]\frac{12}{36} = \frac{13}{39} = \frac{1}{3}[/tex][ 36 divided by 12 is 3 and 39 divided by 13 is 3 ]Thus Option A is correct