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A rectangle has a width of 46 centimeters and a perimeter of 186 centimeters. What is the rectangle's length?

The length is _____ cm.

Answer :

To find the length of the rectangle, let's use the formula for the perimeter of a rectangle:

The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]

We are given:
- The width of the rectangle is 46 centimeters.
- The perimeter of the rectangle is 186 centimeters.

Let's plug these values into the perimeter formula:

[tex]\[ 186 = 2 \times (\text{length} + 46) \][/tex]

To find the length, first simplify the equation:

[tex]\[ 186 = 2 \times \text{length} + 92 \][/tex]

Now, subtract 92 from both sides to isolate the term with the length:

[tex]\[ 186 - 92 = 2 \times \text{length} \][/tex]

[tex]\[ 94 = 2 \times \text{length} \][/tex]

Next, divide both sides by 2 to solve for the length:

[tex]\[ \text{length} = \frac{94}{2} \][/tex]

[tex]\[ \text{length} = 47 \][/tex]

Therefore, the length of the rectangle is 47 centimeters.

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