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 84cm,find the area of the rectangle formed by the wire
Two ways.
1)
L/B = 9:5 or L/B = 9/5 or 5L = 9B
Them L = 9B/5
Since the perimeter is 84, we have
L + L + B + B = 84
9B/5 + 9B/5 + B + B = 84
Solve for B = 15, then L = 27
Area = B X L = ?
2)
Call the sides length = 9x and breadth = 5x
L + L + B + B = 84
9x + 9x + 5x + 5x = 84
Solve for x = 3; then length = 3*9 = 27 and breadth = 3*5 = 15, then area = 27*15 = ?
To find the area of the rectangle formed by the wire, we need to determine the length and breadth of the rectangle.
Let's assume that the length of the rectangle is 9x and the breadth is 5x, where x is a common factor. According to the given information, the ratio of length to breadth is 9:5.
So, the total length of the wire is the sum of all four sides of the rectangle, which can be calculated using the formula: 2(length + breadth).
Accordingly, we have:
2(9x + 5x) = 84 cm
Combine like terms:
28x = 84 cm
Divide both sides of the equation by 28:
x = 3 cm
Now, we can find the length and breadth of the rectangle by substituting the value of x into the equations:
Length = 9x = 9 * 3 = 27 cm
Breadth = 5x = 5 * 3 = 15 cm
Finally, we can calculate the area of the rectangle using the formula: Area = Length * Breadth.
Area = 27 cm * 15 cm = 405 cm²
Therefore, the area of the rectangle formed by the wire is 405 cm².