The height of a door is 2.3 feet longer than it’s width, and it’s front area is 1675.6 square feet. Find the width and height of the door.

Question

answer involes the width of the door in feet and the height in feet. Round to one decimal place as needed. 

Answer 1

Here's what we know:

A = Lw (rectangular area is equal to length times width)

A = 1675.6

L = w + 2.3 (the height (length for purposes of the equation) is 2.3 feet more than width)

 

Plug in the variable-values:

1675.6 = w(w + 2.3)

1675.6 = w² + 2.3w

0 = w² + 2.3w - 1675.6

 

Quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

w = (-2.3 ± √(2.3² - 4 * 1 * -1675.6)) / (2 * 1)

Simplify

w = (-2.3 ± √(5.29 + 6702.4)) / 2

w = (-2.3 ± √6707.69) / 2

w = (-2.3 ± 81.9) / 2 (this is where that rounding need came into play)

w = (-2.3 + 81.9) / 2 ; x = (-2.3 - 81.9) / 2

 

We can't have a negative length/width, so we can throw out the second possibility:

w = ^{-2.3 + 81.9} / ₂

w = ^79.6/₂

w = 39.8

 

Find L:

L = 39.8 + 2.3

L = 42.1

 

Check:

42.1 * 39.8 ≈ 1675.6

1675.58 ≈ 1675.6

Answer 2

It's a BIG door!

 

h = w + 2.3

 

hw = w² + 2.3w = 1675.6

 

The quadratic formula gives w = 39.8 and then h = 42.1.

 

Your should check that these dimensions give the correct area!