# The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle?

Length is

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Let's denote the width of the rectangle as ( w ) inches. Then, the length of the rectangle would be ( 3w ) inches according to the given information.

When the length is increased by 2 inches and the width by 1 inch, the new length becomes ( 3w + 2 ) inches and the new width becomes ( w + 1 ) inches.

The perimeter of a rectangle is given by the formula:

[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) ]

According to the problem, the new perimeter is 62 inches:

[ 62 = 2 \times ((3w + 2) + (w + 1)) ]

Solve this equation for ( w ) to find the width of the rectangle.

[ 62 = 2 \times (4w + 3) ] [ 62 = 8w + 6 ] [ 8w = 62 - 6 ] [ 8w = 56 ] [ w = \frac{56}{8} ] [ w = 7 ]

So, the width of the rectangle is 7 inches.

Now, substitute this value of ( w ) back into the expression for the length to find its value:

[ \text{Length} = 3w ] [ \text{Length} = 3 \times 7 ] [ \text{Length} = 21 ]

So, the length of the rectangle is 21 inches.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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