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in rectangle ABCD, diagonal BD=26 cm and cotangent of angle ABD=1.5. find the area and the perimeter of the rectanglr ABCD

in rectangle ABCD, diagonal BD=26 cm and cotangent of angle ABD=1.5. find the area and the perimeter of the rectanglr ABCD

Grade:9

1 Answers

Arun
25750 Points
5 years ago
Given in the question; 
Cotangent (Cot)ABD = 1.5
can be written as Cot ABD = AB/AD => 3/2 
 


[Cot = Perpendicular/Base] 
=> AB = 3x, AD = 2x 
=> By Pythagoras theorem in right angled triangle ABD 
AB2 + AD2 = BD2
(3x)^2 + (2x)^2 = (26)^2
9x^2 + 4x^2 = 676
x^2 = 676/13
x^2 = 52
x = 2 sqrt13 cm
 
Thus, AB = 3x => 3 × 2 sqrt13
AB = 6 sqrt13
AD = 2x => 2 × 2 sqrt13
AD = 4 sqrt13 
Now Area of rectangle ABCD = AB × AD (length × breadth)
i.e. 6 sqrt13 × 4 sqrt13
=> 24 × 13 
=> 312 cm^2 
And Perimeter of the rectangle = 2 (AB + AD) [2(length + breadth)]
=> 2 (6 sqrt13 + 4 sqrt13)
=> 2 × 10 sqrt13
=> 20 sqrt13 cm
 

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