The perimeter of a rectangular driveway is 68 feet. The area is 280 square feet. What are the dimensions of the driveway?

2 Answers
Nov 21, 2016

1)w=20ft, l=14ft
2)w=14ft, l=20ft

Explanation:

Let's define the variables:

P: perimeter
A: area
l: length
w: width

P=2l+2w=68

Simplify (divide by 2)

l+w=34

Solve for l

l=34-w

A=l*w=280

Substitute 34-w instead of l

A=(34-w)w=280

-w^2+34w=280
-w^2+34w-280=0

Multiply by -1

w^2-34w+280=0

Factorize

(w-20)(w-14)=0

Set each expression equal to zero

1)w-20=0
w=20

2)w-14=0
w=14

Option 1) substitute 20 instead of w

l+w=34
l+20=34
l=14

Option2) substitute 14 instead of w

l+w=34
l+14=34
l=20

1)w=20ft, l=14ft
2)w=14ft, l=20ft

Nov 21, 2016

The dimensions are 20 and 14 feet. See explanation.

Explanation:

We are looking for the dimensions of a rectangle, so we are looking for 2 numbers a and b which satisfy the set of equations:

{(2a+2b=68),(a*b=280):}

To solve this set we calculate b from the first equation:

a+b=34 => b=34-a

Now we substitute b in the second equation:

a*(34-a)=280

34a-a^2=280

-a^2+34a-280=0

Delta=1156-1120=36

sqrt(Delta)=6

a_1=(-34-6)/(-2)=20

a_2=(-34+6)/(-2)=14

Now we have to calculate b for each calculated value of a

b_1=34-a_1=34-20=14

b_2=34-a_2=34-14=20

So we see that the dimensions are 20 and 14 feet.