in a rectangle the length of diagonal is 20 cm more than the length, the area of rectangle is 4800sq. cm. find the perimeter of rectangle?
Answers
Given : in a rectangle the length of diagonal is 20 cm more than the length, the area of rectangle is 4800sq. cm
To find : Perimeter of Rectangle
Solution:
Let say Length of Rectangle = L cm
Then Diagonal = L + 20 cm
& Breadth = Area / length = 4800/L cm
Diagonal² = Length² + Breadth²
=> (L + 20)² = L² + (4800/L)²
=> L² + 40L + 400 = L² + (4800/L)²
=> 40L + 400 = (4800/L)²
=> L + 10 = 4800 * 120 / L²
=> L³ + 10L² - 4800*120 = 0
L = 80
Length = 80
Breadth = 4800/80 = 60
Perimeter of rectangle = 2(80 + 60) = 280 cm
Perimeter of rectangle = 280 cm
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