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A rectangle has length 12x+5 and width 14x+4 . If the perimeter of the rectangle is 42 meters, what are the length and the width of the rectangle?

User Jerika
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Answer:

To find the length and width of the rectangle, we need to set up an equation using the given information.

The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 42 meters.

The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

Let's substitute the given expressions for the length and width into the formula:

42 = 2(12x+5 + 14x+4)

Simplifying the equation, we have:

42 = 2(26x + 9)

Now, let's distribute the 2:

42 = 52x + 18

To solve for x, we can subtract 18 from both sides of the equation:

42 - 18 = 52x

24 = 52x

To isolate x, we can divide both sides of the equation by 52:

x = 24/52

Simplifying the fraction, we get:

x = 6/13

Now that we have the value of x, we can substitute it back into the expressions for the length and width:

Length = 12x + 5

Length = 12(6/13) + 5

Simplifying the expression, we get:

Length = 72/13 + 5

To add the fractions, we need a common denominator of 13:

Length = (72 + 65)/13

Length = 137/13

Width = 14x + 4

Width = 14(6/13) + 4

Simplifying the expression, we get:

Width = 84/13 + 4

To add the fractions, we need a common denominator of 13:

Width = (84 + 52)/13

Width = 136/13

So, the length of the rectangle is 137/13 meters and the width is 136/13 meters.

User Samach
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