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a pair of adjecent sides of a rectangle are in the ratio3:4 and it's diognal is 20cm find the lenth of the sides and hence the perimeter of the rectanlei |
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Answer» The RATIO of the adjacent sides of a rectangle = 3 : 4The adjacent sides of a rectangle are its length and breadth.(adjacent sides = Any two sides with a common end-point are called the adjacent sides of the rectangle)∴ => length : breadth = 3 : 4Let the sides of the rectangle be 3x and 4x (x is a common factor of length and breadth of the rectangle)Given, length of diagonal = 20cmLength of diagonal = √(l² + b²)[Where,l = length of the RECTANGLEB = breadth of the rectangle]=> 20 cm = √(l² + b²)(SQUARING both the sides) :-=> (20)² = l² + b²=> (20)² = (3x)² + (4x)²=> 400 = 9x² + 16x²=> 400 = 25x²=> 16 = x²=> √(16) = x=>x=4Hence, the common factor of length and breadth of the rectangle is 4.Length = 3 x 4 = 12cmBreadth = 4 x 4 = 16cm---------------------------------------------------------------------------------------------------PERIMETER of a rectangle = 2 x (l + b)= 2 x (12 + 16)= 2 x 28= 56 cm--------------------------------------------------------------------------------------------------------Answer :-Length = 12cmBreadth = 16cmThe perimeter of the rectangle is 56 cm. |
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