If a storm window has an area of 400 square inches, what are the dimensions if the window is 12 inches wider than it is high?

1 Answer
Oct 4, 2017
    width                       height

#(6 + 2sqrt(109)) xx(-6 + 2sqrt(109)) #

#26.881 xx 14.881# (3 .d.p.)

Explanation:

Let #x# be the height of the window.

Then the width will be #x+12#.

Since area is width x height we have:

#(x+12)xx x#

This is equal to 400 sq".

So:

#(x+12)xx x=400#

We can write this as:

#x(x+12)=400#

Remove bracket by multiplying it by #x#

#x^2+12x = 400=> x^2+12x-400=0#

Solving using quadratic formula:

#x= (-12 +- sqrt(144-(-1600)))/2#

#x= -6 +-1/2 sqrt(1744)#

#x= -6 +-1/2 sqrt(16 xx109)#

#x= -6 +-1/2(4) sqrt(109)#

#x= -6 +-2 sqrt(109)#

So;: #x= -6 + 2sqrt(109)# or #x= -6 - 2sqrt(109#

We can ignore #x= -6 - 2sqrt(109# since we can't have negative length in this situation.

So dimensions are:

#-6 + 2sqrt(109) xx -6 + 2sqrt(109)+12#

    width                       height

#(6 + 2sqrt(109)) xx(-6 + 2sqrt(109)) #

These will have to be approximate values because of the nature of the square roots. It looks a bit intimidating and most of this work could have been avoided and the answer found solely by calculator, but was done for clarity.