The width of the rectangle is 6 cm less than the length. Find the perimeter and area of the rectangle

The width of the rectangle is 6 cm less than the length. Find the perimeter and area of the rectangle if the width is 4/5 of the length.

Let’s find the length of the rectangle.
Since the width is 6 cm less than the length, it can be written as an expression:

b = a – 6.

Also, the width is 4/5 of the length, which means it can be expressed as:

b = 4/5 * a.

Let’s find what the length is equal to:

a – 6 = 4/5 * a;

a – 6 = (4 * a) / 5;

5 * (a – 6) = 4 * a;

5 * a – 5 * 6 = 4 * a;

5 * a – 4 * a – 30 = 0;

a = 30 (cm).

Let’s find the width of the rectangle:
b = 30 – 6 = 24 (cm).

Find the perimeter of the rectangle:
P = 2 * (a + b) = 2 * (30 + 24) = 2 * 54 = 108 (cm).

Find the area of the rectangle:
S = a * b = 30 * 24 = 720 (cm ^ 2).

Answer: P = 108 cm; S = 720 cm ^ 2.