Final answer:
To find the area of the rectangle with a given perimeter and a relationship between length and width, first express the length in terms of the width, plug this into the perimeter formula, solve for width, then length, and finally calculate the area by multiplying length and width.
Step-by-step explanation:
The perimeter of a rectangle is 130 cm. If the length (L) of the rectangle is 10 cm less than twice its breadth (B), we can write this relationship as L = 2B - 10. The perimeter (P) of a rectangle is given by P = 2L + 2B. By substituting the expression for L into the perimeter equation, we have P = 2(2B - 10) + 2B = 130 cm.
This simplifies to 4B - 20 + 2B = 130, leading to 6B = 150. Thus, B = 25 cm. Now we can find L: L = 2B - 10 = 2(25) - 10 = 50 - 10 = 40 cm. Now that we know both the length and the breadth, we can calculate the area (A) of the rectangle using A = L * B = 40 cm * 25 cm = 1000 cm².
To find the area of a rectangle, first measure or calculate the length and width, then multiply these values. In this example, we followed the steps to find L and B using given relationships and the perimeter, and then calculated the area.