What is the side length of the smallest square plate on which a 30 cm chopstick can fit along a diagonal without any​ overhang? The approximate side length of the square plate is black cm.

21.21 cm

Step-by-step explanation:

Given

length of diagonal on the square is 30 cm

Suppose a is the side length of the square

and length of diagonal is given as

So,

Thus, the side length of the square is 21.21 cm

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for