A pole of height 3 meters is struck by a sledding car and breaks into two pieces such that the first piece is $\frac{1}{2}$ of the second. Find the length of both pieces.

Given :

The total length of the pole $=$ 3m

The length of the first piece is $\frac{1}{2}$ of the second piece.

To do :

We have to find the lengths of the pieces.

Solution :

Let the length of the second piece be 'x' m.

This implies,

The length of the first piece $= \frac{x}{2}$ m.

Therefore,

$x + \frac{x}{2} = 3$

$\frac{(2x+x)}{2} = 3$

$3x = 2(3)$

$3x = 6$

$x = \frac{6}{3}$

$x = 2 $m.

The length of the second piece is 2m and the length of the first piece is $\frac{2}{2} = 1$m.

Therefore, the lengths of the pieces are 1 m and 2 m.

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Updated on: 10-Oct-2022

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