A wire is bent into a rectangle. The ratio of the length of the rectangle to its breadth is 9:5. If the total length of the wire is 84 cm., find the area of the rectangle formed by the wire.

Let's start by assigning variables to the dimensions of the rectangle.

Let L be the length of the rectangle, and let B be the breadth of the rectangle.

The ratio of the length to the breadth is given as 9:5, so we can write:

L/B = 9/5

To solve for the lengths L and B, we need another equation. The total length of the wire is given as 84 cm. We know that the wire forms a rectangle, so:

2L + 2B = 84

Now, let's solve the system of equations to find the values of L and B.

From the ratio equation, we have:

L = (9/5)B

Substituting this into the second equation:

2(9/5)B + 2B = 84

Multiplying through by 5 to eliminate the fraction:

18B + 10B = 420

28B = 420

Dividing both sides by 28:

B = 15

Substituting B = 15 into the ratio equation:

L = (9/5)(15)
L = 27

Therefore, the length of the rectangle is 27 cm and the breadth is 15 cm.

To find the area of the rectangle, we use the formula:

Area = Length x Breadth

Area = 27 cm x 15 cm = 405 cm^2

So, the area of the rectangle formed by the wire is 405 square cm.