The area of two similar triangles XYZ and ABC are 361 cm² and 225 cm², respectively. If the longest side of the larger ΔXYZ be 38 cm, then what is the length (in cm) of the longest side of the smaller ΔABC?

30

By using the property of similar triagle

ΔXYZ and ΔABC is similar triangle. Then ,

\(\frac{Area\;of\; ΔXYZ }{Area \;of \;ΔABC }\) = \(\frac{( Side \;of \;ΔXYZ)² }{( Side\; of\; ΔABC)² }\) 

\(\frac{361 }{225}\) = \(\frac{( 38)² }{( A)² }\)

\(\frac{19 }{15}\) = \(\frac{38 }{A }\)

A = \(\frac{15 × 38 }{19}\)

= 30 cm

So, Length of largest side of triangle ABC = 30 cm