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Answer :
To find the dimensions of the rectangle with a known perimeter and length-to-width ratio, we use the perimeter formula and given ratio to solve for the width and then the length. The rectangle's width is 20 cm, and its length is 40 cm.
To find the dimensions of a rectangle given the perimeter and the ratio of length to width, we need to establish a relationship between these dimensions. Let's denote width as 'w' and length as 'l'. It's given that the length is twice the width, so we can write this as l = 2w.
The formula for the perimeter (P) of a rectangle is P = 2l + 2w. We're given that the perimeter is 120 centimeters, so substituting the relationship between length and width into the perimeter formula, we get 120 = 2(2w) + 2w, which simplifies to 120 = 6w. Dividing both sides by 6, we find w = 20 cm. Therefore, the width is 20 cm, and the length would be twice the width, which is 40 cm.
The dimensions of the rectangle are 20 cm in width and 40 cm in length.
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