If the areas of two similar triangles, ∆PQR and ∆XYZ are 162sq.cm and 200sq.cm respectively. Find the ratio of their perimeters.

Asked by rizwan2959 | 21st Oct, 2018, 12:49: AM

Expert Answer:

The ratio of the perimeters of two similar triangles is same as the ratio of their corresponding sides. 
Also, 
begin mathsize 16px style fraction numerator straight A open parentheses increment PQR close parentheses over denominator straight A open parentheses increment XYZ close parentheses end fraction equals 162 over 200 equals 81 over 100
fraction numerator begin display style straight A open parentheses increment PQR close parentheses end style over denominator begin display style straight A open parentheses increment XYZ close parentheses end style end fraction equals PQ squared over XY squared equals QR squared over YZ squared equals PR squared over XZ squared
fraction numerator begin display style PQ squared end style over denominator begin display style XY squared end style end fraction equals fraction numerator begin display style QR squared end style over denominator begin display style YZ squared end style end fraction equals fraction numerator begin display style PR squared end style over denominator begin display style XZ squared end style end fraction equals fraction numerator begin display style 81 end style over denominator begin display style 100 end style end fraction equals 9 squared over 10 squared
fraction numerator begin display style PQ end style over denominator begin display style XY end style end fraction equals fraction numerator begin display style QR end style over denominator begin display style YZ end style end fraction equals fraction numerator begin display style PR end style over denominator begin display style XZ end style end fraction equals 9 over 10
Hence comma
Ratio space of space perimeter space of space two space similar space triangles space are space in space the space ratio space 9 colon 10. end style

Answered by Sneha shidid | 22nd Oct, 2018, 12:40: PM