High School

If the perimeter of a rectangle is 120 cm and its length is 42 cm, which equation can be used to find the rectangle's width?

A. [tex]w = 120 - 42[/tex]

B. [tex]2w = \frac{120 - 42}{2}[/tex]

C. [tex]2w = 120 - 84[/tex]

D. [tex]w = 120 - 84[/tex]

Answer :

We start with the formula for the perimeter of a rectangle:

[tex]$$
P = 2(\ell + w)
$$[/tex]

Given that the perimeter is [tex]$120\text{ cm}$[/tex] and the length [tex]$\ell$[/tex] is [tex]$42\text{ cm}$[/tex], we substitute these values into the equation:

[tex]$$
120 = 2(42 + w)
$$[/tex]

Next, we expand the right-hand side:

[tex]$$
120 = 84 + 2w
$$[/tex]

To isolate the term in [tex]$w$[/tex], subtract [tex]$84$[/tex] from both sides:

[tex]$$
120 - 84 = 2w
$$[/tex]

Simplifying the left-hand side gives:

[tex]$$
2w = 120 - 84
$$[/tex]

This matches option C.

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