The perimeter of the rectangle is 13 inches, one side is 1.5 inches larger than the other. Find the area of the rectangle.

Let’s introduce a variable denoting the length of one side as x dm, then the length of the second side will be (x + 1.5) dm (based on the condition that one side is 1.5 dm longer than the other).
Let’s recall the formula for finding the perimeter of a rectangle:
P = 2 (a + b);
We substitute the value of the perimeter, as well as the length and width, and proceed to solving the equation:
2 (x + x + 1.5) = 13;
2 (2x + 1.5) = 13;
4x + 3 = 13;
4x = 13 – 3;
4x = 10;
x = 2.5 dm is the length of one side, 2.5 + 1.5 = 4 dm is the length of the second side.
We look for the area by the formula:
S = a * b = 2.5 * 4 = 10 dm ^ 2.