Question

The area of a square can be tripled by increasing the length and width by 10 inches. What is the original length of the square?

Answer 1

The new square has length: 10 + l, where l is the original length of the square, and it's area is (10 + l)^2;
So, we solve the equation: 3 x l^2 = (10 + l)^2;
Then, 3 x l^2 = 100 + 20 x l + l^2;
Finally, 2xl^2 - 20xl - 100 = 0;  / ÷2;
l^2 - 10l - 50 = 0 (we use the quadratic equation formula);
The only positive solution is l = 5(1+ \sqrt{3} );