Question

The diagonal of a rectangle is √125125 cm and its area is 50 sq. cm. The perimeter of the rectangle must be एक आयत का विकर्ण √125125 सेमी है और इसका क्षेत्रफल 50 वर्ग सेमी है। आयत की परिधि होनी चाहिए



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Answer 1

Answer:

Let l be the length and b be the breadth

l × b = 50.....(1)

l^2 + b^2 = 125....(2)

from (1) l = 50/b

put this value of l in (2)

(50/b)^2 + b^2 = 125

2500 + b^4 = 125b^2

b^4 -125b^2 + 2500 = 0

b^4 - 100b^2 - 25b^2 + 2500 = 0

b^2(b^2 - 100) - 25(b^2 - 100) = 0

(b^2 - 25)(b^2 - 100) = 0

b^2 - 25 = 0, b^2 = 25, b = 5

b^2 -100= 0, b^2 = 100, b = 10

If b = 5, then l = 10

perimeter = 2(10+5) = 30 Ans