High School

The length of a rectangle is 3 cm more than twice that of its width. The rectangle has a perimeter of 120 cm.

Find the length and width of the rectangle.

Answer :

Final answer:

To find the length and width of a rectangle when given its perimeter and a relation between its length and width, we can write and solve an equation. The length of the rectangle is found to be 41 cm and the width is 19 cm.

Explanation:

To solve this problem, let's first assign variables to the length and width of the rectangle. Let the width be x cm. According to the problem, the length is 3 cm more than twice the width, so the length would be 2x + 3 cm. The formula for the perimeter of a rectangle is 2(length + width), so we can write the equation as:

2(2x + 3 + x) = 120

4x + 6 + 2x = 120

6x + 6 = 120

6x = 114

x = 19

So the width of the rectangle is 19 cm. Substituting this value into the expression for the length, we get:

length = 2(19) + 3 = 41 cm

Therefore, the length of the rectangle is 41 cm and the width is 19 cm.

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