Question

The number of trees in each row of a garden is equal to the number of rows in the garden. After 111 trees have uprooted in a storm there remain 10914 trees in the garden. The number of rows of trees in the garden is
A) 100
B) 105
C) 115
D) 125

Answer 1

Hint: Here, we’ll use the concept of squares and square root to solve this question. we’ll first add the total number of trees that is 111 and 10914 and then find the square root of it.

Complete step by step solution:
We will answer here that the number of trees is equal to the number of rows.
Therefore, let the number of rows and the number of trees be x
This means that
number of rows = number of trees = x
The total no. of trees = 10914 + 111 = 11025
11025 is the total number of trees before the trees have been uprooted in a storm.

Therefore the total number of rows $x\times x={{x}^{2}}$
Now, equating total number of rows with the total number of trees, we get
.\[\begin{align}
  & or,{{x}^{2}}=11025 \\
 & or,x=\sqrt{11025} \\
 & or,x=\sqrt{\underline{3\times 3}\times \underline{5\times 5}\times \underline{7\times 7}} \\
 & or,x=\sqrt{{{3}^{2}}\times {{5}^{2}}\times {{7}^{2}}} \\
 & or,x=3\times 5\times 7 \\
 & or,x=105 \\
\end{align}\].
Hence, the number of rows of trees = x = 105

B is the answer to this question

Note: In this type of question first count the total number of trees and equation their row and total tree count and then square root the total trees will give the answer. Students who are familiar with the concept of matrix and determinants can also think of the solution with that concept. It’s recommended to visualise or better understand the question with different concepts.