15. Seventeen year and thirteen year locusts both emerged in 1971. When will be the
next time they both emerge in the same year?

221 years or in the year 2192

Step-by-step explanation: The 13-year locusts emerge after every 13 years, that is, after every year that is a multiple of 13. The 17- year locusts emerge after every 17 years, that is, after every year that is a multiple of 17. Therefor, if both 13- and 17- year locusts happened to emerge in 1971, such interference would repeat after every x years, where x is a common multiple of 13 and 17. The next interference would occur after the number of years which is the least common multiple of 13 and 17.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl