Question

A piece of string is 40 cm long it is cut into three pieces .The longest piece is 5 cm more than twice as long as the middle-sized and the shortest is half of the middle piece. Find the length of the longest piece

Answer 1

Step-by-step explanation:

Let x, y and z be the three pieces of the string, where x is longest and z is shortest.

$\therefore \: x + y + z = 40.....(1) \\ other \: conditions: \\ x = 2y + 5.....(2) \\ and \\ z = \frac{y}{2}.....(3) \\ From \: equations \: (1), \: (2) \: and \: (3) \\ (2y + 5) + y + (\frac{y}{2}) = 40 \\ \therefore \: 3y + 5 + \frac{y}{2} = 40 \\ \therefore \frac{6y + 10 + y}{2} = 40 \\ \therefore \frac{7y + 10 }{2} = 40\\ \therefore7y + 10 = 40 \times 2 \\ \therefore7y + 10 = 80 \\ \therefore7y = 80 - 10\\ \therefore7y = 70 \\ \therefore \: y = \frac{70}{ 7} \\ \therefore \: y = 10 \\ \implies \: x = 2 \times 10 + 5 \\ \implies \: x = 20 + 5\\ \huge \orange {\boxed{\implies \: x = 25 \: cm}}$

Hence, length of the longest piece is 25 cm.