The semi-perimeter of a rectangle is 29 cm. The width is 21 cm less than the length

The semi-perimeter of a rectangle is 29 cm. The width is 21 cm less than the length. Determine the perimeter of a square that has the same area.

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

2. Let’s compose two equations:

(1) a + b = 29;

(2) a – b = 21;

3. Add these equations:

a + b + a – b = 50;

2a = 50;

a = 25 cm.

h = 29 – a = 29 – 25 = 4 cm.

4 . We calculate the area (S) of a given rectangle:

S = a x h = 25 x 4 = 100 cm².

5. The area of the square (S) is also 100 cm².

6. The length of the side of this geometric figure is √S = √100 = 10 cm.

We calculate the perimeter of the square (P):

P = 4 x 10 = 40 cm.

Answer: the perimeter of the square is 40 cm.