Question

a straight wooden stick of length 25 cm is cut into 5 parts whose length are in AP the sum of the square of each part is 135 find the length of each part​

Answer 1

let lengths be x, x+1, x+2, x+3, x+4

according to given condition:

(x^2)+(x+1)^2+(x+2)^2+(x+3)^2+(x+4)^2= 135

x=5

length of each part will be 5 cm, 6 cm, 7 cm, 8 cm and 9 cm respectively.

Answer 2

Answer:

Length of each part will be 3 cm, 4 cm, 5 cm, 6 cm and 7 cm

Step-by-step explanation:

Given a straight wooden stick of length 25 cm is cut into 5 parts whose length are in AP the sum of the square of each part is 135.

we have to find the length of each part​

Let lengths be x-2d, x-d, x, x+d, x+2d

According to given condition:

(x-2d)+(x-d)+x+(x+d)+(x+2d)=25

⇒ 5x=25 ⇒ x=5

Also given the sum of the square of each part is 135

⇒ $(x-2d)^2+(x-d)^2+x^2+(x+d)^2+(x+2d)^2=135$

⇒ $(x^2+4d^2-4xd)+(x^2+d^2-2xd)+x^2+(x^2+d^2+2xd)+(x^2+4d^2+4xd)=135$

⇒ $10d^2=10$

⇒ $d=\pm 1$

which gives the AP 3, 4, 5, 6, 7

hence, the length of parts are

x-2d=5-2(1)=3

x-d=5-1=4

x=5

x+d=5+1=6

x+2d=5+2(1)=7

if take d=-1 the result will be same as above

∴ length of each part will be 3 cm, 4 cm, 5 cm, 6 cm and 7 cm