Question

A rectangular driveway has an area of 880 square feet and a perimeter of 128 feet. What are the dimensions of the driveway?

Answer 1

Answer:

Dimensions are 20 X 44 feet

Step-by-step explanation:

First we need to build two equations:

For area X times Y = 880

For Perimeter 2x + 2y = 128

Now we need to solve one so we can substitute it into the other:

2x + 2y = 128 becomes

2x = 128 - 2y and then

x = 64 - y We will substitute this into the are equation

(64 - y)y = 880

64y - $y^{2}$ = 880

-$y^{2} + 64y -880 = 0$

factor out the negative

-($y^{2} - 64y +880 = 0$

Factor:

-(y - 20)(y - 44) = 0

y-20 = 0 and y - 44 = 0

y = 20 and y = 44

Plugging these in two both of our formulas works

20 X 44 = 880 for area

2(20) + 2 (44) = 128 for perimeter