Question

The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100, find the length and

width of the rectangle.
If /= length and w=width, which of the following systems could be used to solve the problem?
0/=3 w+ 2 and 2 /+ 2 w=100
O/+2=3 wand 2 /+ 2 w=100
O/ 2 w+3 and 2 / +2 = 100

Answer 1

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Explanation:

To solve this problem, we need to set up a system of equations that represents the given information.

The first equation represents the relationship between the length and width of the rectangle: / = 3w + 2.

The second equation represents the fact that the perimeter of the rectangle is 100: 2 / + 2w = 100.

The third equation is not valid because it has a missing variable on the left side.

Therefore, the correct system of equations to use to solve this problem is:

/ = 3w + 2

2 / + 2w = 100

To solve this system, we can first substitute the expression for / in the first equation into the second equation, resulting in:

(3w + 2) + 2w = 100

5w + 2 = 100

5w = 98

w = 19.6

Then, we can substitute this value for w back into the first equation to find the value of /:

/ = 3(19.6) + 2 = 59.8 + 2 = 61.8

Therefore, the dimensions of the rectangle are / = 61.8 and w = 19.6.

I hope this helps! Let me know if you have any questions.