algebra 2 math question

Question

The height of a door is 2.3 feet longer than its​ width, and its front area is 1539.2 square feet. Find the width and height of the door.

Answer 1

1539.2 = w(w+2.3= w^2+ 2.3w

use the quadratic formula

x= (-b+/-sqr(b^2-4ac))/2a where

x=w, a=1, b=2.3, c=-1539.2

ignore the negative square root

w= -2/2+(1/2)sqr(2.3^2+4(1539.2)= about 38.1 feet wide

height = about 40.4 feet long

40.4 x 38.1 = 1539.2