Question

A uniform wire of length 4 ��� is bent into the shape of a letter l. The upright part of the wire is ______ times as long as the base of the l.

Answer 1

The upright part of the wire is
`\((4 - x)/(x)\)` times as long as the base of the letter "L.".

To determine the relationship between the upright part and the base of the letter "L," we can set up an equation based on the given information.

Let's assume that the base of the letter "L" is represented by the horizontal part of the wire, and the upright part is the vertical part.

Let
`\( x \)` be the length of the horizontal part (base) of the letter "L," and
`\( y \)` be the length of the vertical part (upright).

Given that the total length of the wire is \( 4 \) meters, we can express this as an equation:

`\[ x + y = 4 \]`

Now, we are asked to find the relationship between the upright part
`(\( y \))` and the base
`(\( x \))`. We want to find
`\( y/x \)`.

Divide both sides of the equation by
`\( x \)`:

`\[ (x)/(x) + (y)/(x) = (4)/(x) \]`

Simplify:

`\[ 1 + (y)/(x) = (4)/(x) \]`

Subtract
`\( 1 \)` from both sides:

`\[ (y)/(x) = (4)/(x) - 1 \]`

Combine the terms on the right side:

`\[ (y)/(x) = (4 - x)/(x) \]`

Therefore, the upright part of the wire is
`\((4 - x)/(x)\)` times as long as the base of the letter "L."

Answer 2

The upright part of the wire is (4 - x) / x times as long as the base of the L.

Step-by-step explanation:

In this problem, we have a uniform wire of length 4 units that is bent into the shape of a letter L. We need to find the ratio of the length of the upright part of the wire to the length of the base of the L.

Let's assume that the length of the base of the L is x units. Since the wire is uniform, the remaining length of the wire after the base of the L is the same as the length of the upright part of the wire.

Therefore, the length of the upright part of the wire is 4 - x units. Now we can set up the ratio:

(4 - x) / x

And that's our answer. The upright part of the wire is (4 - x) / x times as long as the base of the L.