A straight wooden stick of length 25cm is cut into 5 parts whose lengths are in ap The sum of the squares of each part is 135 find the length of each part
Answers
Answer:
the length of the parts will be 3,4,5,6,7 cm respectively.
Step-by-step explanation:
Let the length of the first part = a
let the common difference of AP = d
hence,
2nd part = a + d
3rd part = a + 2d
4th part = a + 3d
5th par = a + 4d
Given sum of these parts is 25
=> a + (a+d) + (a+2d) + (a+3d) + (a+4d) = 25
=> 5a + 10d = 25
=> a + 2d = 5.......................eqn1
Given square of these parts is 135
=> a² + (a+d)² + (a+2d)² + (a+3d)² + (a+4d)² = 135
=> a² + a² + d² + 2ad + a² + 4d² + 4ad + a² + 9d² + 6ad + a² + 16d² +8ad = 135
=> 5a² + 30d² + 20ad = 135
=> a² + 6d² + 4ad = 27
=> a² + 4d² + 4ad + 2d² = 27
=> (a+2d)² + 2d² = 27
=> 5² + 2d² = 27
=> 2d² = 27 - 25 = 2
=> d² = 1
=> d = 1
putting the value of d in eqn 1,
a + 2 = 5
=> a = 3
Hence the length of the parts will be;
1st part = a = 3 cm
2nd part = a + d = 3 + 1 = 4 cm
3rd part = a + 2d = 3 + 2 = 5 cm
4th part = a + 3d = 3 + 3 = 6 cm
5th par = a + 4d = 3 + 4 = 7 cm
Answer: the five parts are 3, 4, 5, 6 and 7 cm in length respectively
Step-by-step explanation:
Let the five parts the a A A plus the