the height of a door is 2.2 feet longer than its width, and its front area is 1647.2 square feet. Find the width and height of the door?

h=2.2+w

s=h.w

1647.2=h.w

h=1647.2/w

1647.2/w=2.2+w

1647.2=2.2w+w²

w²+2.2w-1647.2=0

By Bhaskara:

w'=39.5

w''=-41.7....non serve

h=39.5+2.2=41.7

Answer:

w=39.5 feet

h=41.7 feet

This is really dumb. I don't know why teachers or text books give such goofy numbers to work with when the same problem could be asked testing your knowledge of the concept using less arduous numbers. Anyway, Smug, this is pretty simple. It's just that the solution involves the use of the quadratic equation.

Here's the thing, if the area of a quadrilateral is simply the with times the height, then in this problem the width (x) times the height (x + 2.2) equals the area (1647.2).....It's just like if the width were 2 and the height were 2 + 2, then the area would be 2 times 4 and equal 8. So to solve this we have:

(x)(x+ 2.2) = 1647.2 which is x^2 + 2.2x = 1647.2, and rearranging this and placing into quadratic form is:

x^2 + 2.2x - 1647.2 = 0..........using the quadratic formula and solving for x equals 39.5 ft. and x +2 equals 41.7 ft. To check this answer just multiply the width time the height. As I've said, this is dumb; I suppose the idea is to give you practice using the quadratic formula, but it could have been done without giving you such goofy numbers, for example leaving off the tenths number.