Answer :
Final answer:
The width of the frame is 25 inches and the length is 20 inches which are found by setting up and solving two simultaneous equations: one for the perimeter of the rectangle and the other representing the relation between length and width.
Explanation:
To find the length and width of the frame, we need to set up equations based on the given information. We know the perimeter of the frame is 120 inches and the length is thirty less than twice the width. Therefore, we can set up the following equations:
- The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. Plugging in the given perimeter, we get 120 = 2l + 2w.
- It's also stated that the length is thirty less than twice the width, so we have l = 2w - 30.
The next step is to solve these equations together to find the lengths of l and w. We can substitute equation 2 into equation 1 to find: 120 = 2*(2w - 30) + 2w. Simplifying this, we find that the width of the frame is 25 inches. Then, substituting w = 25 inches into the equation l = 2w - 30, we find that the length of the frame is 20 inches.
Learn more about Simultaneous Equations here:
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