Final answer:
By using the perimeter formula for a rectangle and substituting the given values, we can determine that the breadth of the rectangle is 6m and the length is 14m, resulting in an area of 84m². The correct answer is C.
Step-by-step explanation:
To solve the problem of finding the length and breadth of a rectangle where the length is 8 more than its breadth and its perimeter is 40m, we use two key equations. The perimeter (P) of a rectangle is given by P = 2(length + breadth), and in this case, we're told the perimeter is 40m. If breadth = b, then the length is length = b + 8.
First, plug in these expressions into the perimeter equation:
- 2(b + (b + 8)) = 40
- 2(2b + 8) = 40
- 4b + 16 = 40
- 4b = 24
- b = 6m
So the breadth is 6m, and the length is 6m + 8m = 14m.
To find the area, we use the equation Area = length * breadth. Thus:
- Area = 14m * 6m
- Area = 84m²
The correct answer is: Length = 14m, Breadth = 6m, Area = 84m², which corresponds to option c.