quadratic equation

Question

The heaviest reported door in the world is the 708.6 ton radiation shield door in ... shield door in the National Institute for Fusion Science at Toki, Japan. If the height of the door is 1.1 feet longer than its width, and its front area (neglecting depth) is 1439.9 square feet, find its width and height [Interesting note: the door is 6.6 ...

Answer 1

Assume door height is h and width is w

h = w + 1.1

w x h = 1439.9

w = 1439.9/h

Substitute into first equation

h = 1439.9 / h + 1.1

multiply left and right by h then bring every thing to the left while changing signs:

h^2 - 1.1 h - 1439.9 = 0

which is a quadratic equation

h = (1.1 +/- sqrt(1.1^2 + 4 x 1439.9))/(2 x 1) = 38.5 ft and w = 1439.9/38.5 = 37.4 ft

The second answer will lead to h being smaller than w, therefore is rejected.