



 
Rajesh, There is not enough information to solve this problem. I let the length of the rectangle be $L$ cm, its breadth be $B$ cm and the hypotenuse of the triangle be $H$ cm. You want $2L + 2B = 12 + B + H.$ Since the triangle is a right triangle, from Pythagoras' Theorem you know that $12^2 + B^2 = H^2 .$ To illustrate that there is not enough information let $B = 5$ cm. Then using Pythagoras' Theorem $H = 13$ cm and the perimeter of the triangle is $12 + B + H = 30$ cm. Since the perimeter of the rectangle is also 30 cm you must have $L = 10$ cm. Now suppose $B = 7$ cm then Pythagoras' Theorem gives $H = 13.89$ cm which means $L = 9.45$ cm. Now you try one, say $B = 15$ cm. What do you get for $L?$ There are many possible values for $L.$ Is there something missing in your wording of the problem? Penny  


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 