A scale drawing of a rectangular object has a scale of 1 in. : 3 ft. The scale drawing has a length of 5 inches. What is the actual length?

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} );