The perimeter of the rectangle is 164 cm and the width is 34 cm. How much longer is the length than the width?

P = 164 cm.
b = 34 cm.
a =? cm.
Let’s use the formula for the perimeter of a rectangle:
P = 2 (a + b);
We substitute the values ​​of known quantities into the formula.
We get a linear equation with one variable.
164 = 2 (a + 34);
On the right side of the equation, we open the brackets according to the distribution law of multiplication.
164 = 2a + 68;
To find the unknown term, it is necessary to subtract the known term from the sum.
2a = 164 – 68;
2a = 96;
To find an unknown factor, you need to divide the product by a known factor.
a = 96: 2;
a = 48.
a – b = 48 – 34 = 14 (cm).
Answer: The length of the rectangle is 14 centimeters longer than the width.