Question

On fifth June ie on world environment day, the Mathematies teacher ask the students of standard X to plant 300 trees in rows, to form an isosceles triangle, the mumber of trees in the successive rows increasing by one from the apex to the base. How many trees the students have to plant in the row which forms the base of the triangle ?



please answer me it is very urgent​

Answer 1

Step-by-step explanation:

total number of trees to be planted = 600

first row that is the apex has 1 plant

subsequent row has 1 plant more

first row 1 plant

second row 2 plant

third row 3 plant

and so on

therefore the first term = a = 1

common difference = d = 1

total sum = Sn = 600

this is an arithmetic progression of series

$sn = \frac{n}{2} (2a + (n - 1)d) \\ 300 = \frac{n}{2} (2(1) + (n - 1)(1)) \\ 300 \times 2 = n(2 + n - 1) \\ 600 = {n}^{2} + n \\ {n}^{2} + n - 600 = 0 \\ {n}^{2} - 24n + 25n - 600 = 0 \\ n(n - 24) + 25(n - 24) = 0 \\ (n - 24)(n + 25) = 0 \\ n - 24 = 0 \: \: \: \: \: \: \: n + 25 = 0 \\ n = 24 \: \: \: \: \: \: \: \: n = - 25$

as the number of rows cannot be negative we take n = 24

therefore the number of rows to plant 300 tree is 24

an = a + (n-1)d

a24 = 1 + (24-1)(1)

a24 = 1 + (23)(1)

a24 = 1 + 23

a24 = 24

the base of the triangle has 24 trees

hope you get your answer