ABC and XYZ are two similar triangles with \( \Large \angle C\) = \( \Large \angle Z\), whose areas are respectively 32 and 60.5. If XY = 7.7 cm, then what is AB equal to?

For similar triangles, ratio of areas is equal to the ratio of the squares of any two corresponding sides. .



Here, \( \Large \frac{area\ of\ \triangle ABC}{area\ of \triangle XYZ} = \frac{AB^{2}}{XY^{2}} \)

=> \( \Large \frac{32}{60.5} = \frac{AB^{2}}{ \left(7.7\right)^{2} } \)

=> \( \Large \frac{32 \times 59.29}{60.5} = AB^{2} \)

=> \( \Large 31.36 = AB^{2} \)

\( \Large \therefore AB= \sqrt{31.36} = 5.6 cm \)