The areas of two similar triangles ABC and PQR are 64 cm² and 144 cm², respectively. If the greatest side of the smaller △ABC is 24 cm, then what is the greatest side of the bigger △PQR?

36 cm

Concept Used

The similarity of triangles = If two triangles are similar, then their corresponding angles are congruent and corresponding angles are congruent and corresponding sides are equal in proportion.

Ratio of area of similar triangles = (ratio of sides of the triangles)²

Calculations

Let the greatest side of the bigger \(\Delta \)PQR be x

Greatest side of the smaller \(\Delta \)ABC = 24 cm

According tot the question,

Ratio of the area of triangles = 64 : 144

As we know that

Ratio of the triangles = (ratio of sides of the triangles)²

= \(\frac{64}{144}\) = \(\frac{24}{x}\)²  

= \(\frac{8}{12}\) = \(\frac{24}{x}\)

= x = 36 cm.

Therefore, greatest side of the bigger \(\Delta \)PQR is 36 cm.