What number is the area of a rectangle whose length is six times its width if its perimeter is equal to a square with an area of 46cm²?

Let the width of this rectangle be X cm, then its length will be 5X cm (5 times more).

P rectangle = P square by condition.

Let’s write the formulas for finding the perimeters for these figures:

P rectangle = 2 * (a + b); (where a – length; b – width).

P square = 4a.

Now let’s write down the formulas for finding the area for a rectangle and a square:

S rectangle = a * b.

S square = a ^ 2.

S square, by condition, 36 cm ^ 2.

Consequently, the side of the square is:

a = √36 = 6 centimeters.

Consequently,

P square = 6 * 4 = 24 centimeters.

P rectangle = 24 centimeters.

24 = 2 * (a + b);

a + b = 12.

5X + X = 12;

6X = 12;

X = 2.

The width is 2 centimeters.

Length = 2 * 6 = 12 (centimeters).

S rectangle = 12 * 2 = 24 cm ^ 2.