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The perimeter of a rectangle is 36 ft. The length is 10 ft. longer than the width.

Find the dimensions. Write a system of linear equations and solve the resulting system. Let x be the length and y be the width.

The first equation 2x+2y=?

The second equation x=y+?

What is the length in ft.?

What is the width in ft.?

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1 Answer


Your first equation is correct for the perimeter: 2x+2y=36

The second equation requires you to translate "The length is 10 ft. longer than the width"

Using x as length and y as width, we can translate the sentence: x is 10 ft. longer than y

Generally, "is" means the "=" sign, so x = 10 ft. longer than y

and finally longer than usually translates to addition "+" or x = 10+y

To solve the two equations, I would recommend substituting the second equation's y+10 into the first equation for x, i.e. 2(y+10) + 2y = 36.  I'll leave solving this for you, but feel free to email me or ask a follow-up if you do not understand this part.

Once you solve this for y (the width), you then can add 10 to y to find the length (x).