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The length and breadth of a rectangle are in the ratio 9:5. if its area is 720m, find its perimeter.

(a) 112 metre
(b) 115 metre
(c) 110 metre
(d) 118 metre
(e) None of these

User HandMadeOX
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1 Answer

2 votes

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.

User Kim Larsen
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