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If the perimeter of a rectangle is 46 and diagonal is 17 then what is the area of the rectangle?

Option:
A. 30
B. 60
C. 120
D. 180
Answer: C . 120

Justification:

Perimeter of the rectangle is = 2 (l + b) = 46 => l + b = 23

Diagonal of the rectangle is = l^2 + b^2 = (17)^2 = 289.

Area of the rectangle is l * b.

 

Now diagonal of the rectangle is = l^2 + b^2 = 17^2 = 289

=> 289 + 2*l*b = l^2 + b^2 + 2lb = (l+b)^2 = 23^2 = 529

=> 2*l*b = 529-289 = 240

=> l*b = 240/2 =120

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