In the given figure, area of the triangle ABC is 80 cm² and BC = 10 cm, then what is side (in cm) of the square PQRS?

Area of the triangle ABC = 1/2 × BC × Height

⇒ 80 = 1/2 × 10 × Height

⇒ Height = 16 cm

We know that side of the square PQRS, all the sides are equal

Now, SR|| BC and Let M is the intersection point of sides SR and AD.

So, △ASR ∼ △ ABC    (From reverse of Thales' theorem)

⇒ \(\frac{{BC}}{{SR}} = \frac{{AD}}{{AM}}\)

⇒ \(\frac{{10}}{{x}} = \frac{{16}}{{16 - x}}\)

⇒ x = 80 /13

∴ The correct answer is 80/13.