Final answer:
To find the perimeter of a rectangle where the length and breadth are in a 9:5 ratio and the area is 720m², assume the length as 9x and breadth as 5x, solve for x, and then calculate the perimeter using the formula P = 2(length + breadth). The perimeter is (a) 112 meters.
Step-by-step explanation:
To find the perimeter of a rectangle when the length and breadth are given in a ratio and the area is known, we can use the formula for area (Area = length × breadth) to first find the dimensions and then apply the perimeter formula (Perimeter = 2(length + breadth)).
Let us assume that the length (ℒ3) is 9x and the breadth (ℒ) is 5x. The area of the rectangle is given as 720 square meters, which means:
9x × 5x = 720
45x² = 720
x² = 720 / 45
x² = 16
x = 4 (since x is positive, we take the positive square root)
Therefore, the length is 9x = 9 × 4 = 36 meters, and the breadth is 5x = 5 × 4 = 20 meters.
The perimeter (P) of the rectangle can be calculated as follows:
P = 2(length + breadth) = 2(36 + 20) = 2(56) = 112 meters
So, the correct answer is (a) 112 meters.