The length of the side AB of the rectangle is 12 cm longer than the side BC by 12 cm. If the length of AB is increased

The length of the side AB of the rectangle is 12 cm longer than the side BC by 12 cm. If the length of AB is increased by 13 cm and the length of BC is increased by 6 times, you will get equal results. Find the length AB.

1. Let’s designate the length of the side AB of the rectangle by the index “a”, the length of the side BC by the index “b”.

2. Let’s compose two equations:

(1) a – b = 12;

(2) (a + 13) = 6b; a – 6b = – 13;

3. Subtract the second equation from the first equation:

a – b – a + 6b = 25;

5c = 25;

h = 5 centimeters.

4. Substitute the value at = 5 into the first equation:

a – 5 = 12;

a = 12 + 5 = 17 centimeters.

Answer: the length of the AB side is 17 centimeters.