A rectangular classroom is 4 feet wider than it is long and has an area of 480 square feet. What is the length of the classroom in feet?

Question

I need help on my homework 

Answer 1

Let x = length 

 

The width is 4 feet wider than length so that would be x + 4

 

Area of a rectangle is length times width.

 

x(x + 4) = 480

 

Distribute the x

 

x² + 4x = 480

 

Subtract 480 from both sides

 

x² + 4x - 480 = 0

 

Factor this quadratic

 

(x + 24)(x - 20) = 0

 

set each factor equal to zero and solve each

 

x + 24 = 0             x - 20 =  0

 

        x = -24               x = 20

 

Since a length can't be negative we eliminate the -24 answer.

 

The only answer for the length is 20.

 

width = x + 4 = 20 + 4 = 24

 

CHECK

 

area = length times width

 

480 = (20)(24)

 

480 = 480  √

 

An unusual set of numbers since usually the length is the longer dimension.

 

 

 

 

Answer 2

l=length

l+4=width

A=lw

480=l(l+4)

480=l^2+4l

l^2+4l-480=0

480=2*2*2*2*2*3*5=(2*2*2*3)*(2*2*5)=24*20 and 24-20=4, the coefficient of the middle term

factor

(l+24)(l-20)=0

l-20=0

l=20 feet is the length

l+4=24 feet is the width

seeing that A=l*w you are basically looking for two numbers that differ by 4 and whose product is 480

all you had to do was factor 480 to get the answer

480=2*2*2*2*2*3*5 and rearrange the factors to get the two numbers that differ by 4

rearranging....

480=(2*2*2*3)*(2*2*5)=24*20=480 and 24-20=4