SOLUTION: Find the dimensions of a rectangle whose length is 2 cm more than twice its width and which has a diagonal of 13 c

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Question 1003747: Find the dimensions of a rectangle whose length is 2 cm more than twice its width and which has a diagonal of 13 c
Answer by parassingh(1) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length be l and the width be b.
Now, l= 2b +2 is given.
According to pythagoras theorem
(diagonal)^2= l^2 + b^2
so, 13*13= l*l + b*b;
169= (2b+2)(2b+2) + b*b;
169= 4(b+1)(b+1) + b^2;
169= 4(b^2 + 2b + 1) + b^2;
169= 5b^2 + 8b + 4;
5b^2 + 8b - 165 = 0;
5b^2 + 33b - 25b -165 =0;
b(5b +33) - 5(5b + 33) = 0;
(b - 5)*(5b + 33) = 0;
so, b=5;
l= 2b+2 = 10+2= 12;
so, l=12, b=5;