# The rectangle is 3 cm longer than wide and has a perimeter of 22 cm. Find the length and width using

August 30, 2021 | education

| **The rectangle is 3 cm longer than wide and has a perimeter of 22 cm. Find the length and width using the substitution method.**

Given a rectangle.

Let x be the width of the rectangle.

Since the length of the rectangle is 3 cm longer than the width, then the length of the rectangle is 3 * x.

The perimeter is 22 cm.

Find the width and length of the rectangle.

P = 2 * (a + b);

P = 2 * (x + 3 * x);

22 = 2 * 4 * x;

2 * 11 = 2 * 4 * x;

1 * 11 = 1 * 4 * x;

11 = 4 * x;

x = 11/4;

x = 2.75.

Then:

3 * x = 3 * 11/4 = 3 * 2.75 = 8.25.

From this we find that the width of the rectangle is 2.75 cm and the length of the rectangle is 8.25 cm.

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