The sum of the length and width of the rectangle is 14cm. The length is 4 cm more than the width. Find the area.

Let’s take the length of the rectangle for a and the width for b.
1) based on the condition, we will compose two equations:
1.a + b = 14,
2. a – b = 4;
2) express a from the first equation through b and substitute the value into the second equation:
a = 14 – b,
(14 – b) – b = 4,
14 – 2 b = 4,
2 b = 14 – 4,
2 b = 10,
b = 10: 2,
b = 5 cm – the width of the rectangle;
3) define the length of the rectangle:
a = 14 – b = 14 – 5 = 9 centimeters;
4) calculate the area of the rectangle:
S = a b = 9 * 5 = 45 square centimeters.
Answer: S = 45 cm ^ 2.