Answer:
length = 20 feet
width = 7 feet
Explanation:
This problem can be solved using a system of equations. Using the given information, you can formulate 2 equations:
l*w = 140
l = 2w + 6
In order to solve this system of equations, you can use the Substitution Property of equality to substitute the l in the first equation for (2w + 6) in order to find the width:
where l*w = 140 and l = 2w + 6,
1. (2w + 6)*w = 140
2. 2w^2 + 6w = 140
3. w^2 + 3w = 70
4. w^2 + 3w - 70 = 0
5. (w - 7) (w + 10) = 0
6. w = 7, -10
1. Substitution
2. Simplification
3. Divide both sides by 2
4. Subtract 70 from both sides
5. Factor the left side (find 2 numbers that add to 3 and multiply to -70)
6. Solve for w
The width must be 7 because a width of -10 is impossible. Now, you just need to plug that into the equation to solve for l:
l*w = 140
7l = 140
l = 20
That means that the length is 20 and the width is 7.