## YanaSidlinskiy one year ago The floor of a shed has an area of 99 square feet. The floor is in the shape of a rectangle whose length is 7 feet less than twice the width. Find the length and the width of the floor of the shed. Use the formula, area=length*width

1. YanaSidlinskiy

length is 7 feet less than twice the width = 7-2x? Something like that...

2. mathstudent55

width = w twice the width: 2w 7 ft less than twice the width: 2w - 7

3. mathstudent55

A = LW = w(2w - 7) = 99

4. YanaSidlinskiy

WAIT! I want to solve it lol. I need to understand it on my own on how to do it haha. Wait, why would it matter if I put it the way you showed me?

5. mathstudent55

There is a difference in the way you write it. Let me explain. Let's say Mary is 16 years old and Jane is 18 years old. You can say Mary's age is 2 years less than Jane's age. If that means 18 - 2, then Mary is 16 years old which is correct. If mistakenly you think that means 2 - 18 = -16, then Mary is -16 year old which is meaningless.

6. mathstudent55

"7 less than 2w" is 2w - 7 "7 less" means subtract 7, take away 7, from 2w 7 - 2w is "2w less than 7"

7. YanaSidlinskiy

Gotcha! Ok, makes sense. Lemme solve this real quick. Sorry if it'll take a while..

8. mathstudent55

9. YanaSidlinskiy

I got 22.

10. mathstudent55

w(2w - 7) = 99 2w^2 - 7w - 99 = 0

11. YanaSidlinskiy

That's what I had in the first place..

12. mathstudent55

$$\large x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}$$ $$\large w = \dfrac{7 \pm \sqrt {(-7)^2 - 4(2)(-99)}}{2(2)}$$ $$\large w = \dfrac{7 \pm \sqrt {49 + 792}}{4}$$ $$\large w = \dfrac{7 \pm \sqrt {841}}{4}$$ $$\large w = \dfrac{7 \pm 29}{4}$$ $$\large w = \dfrac{36}{4}$$ or $$w = \dfrac{-22}{4}$$ $$\large w = 9$$ or $$\large w = -5.5$$

13. mathstudent55

Since a width cannot be negative, we discard w = -5.5. The width is 9 ft. The length is 2w - 7 = 2(9) - 7 = 18 - 7 = 11 ft

14. YanaSidlinskiy

It's the minor stuff that kills me lol.

15. mathstudent55

You need to work carefully. I went through the same, making stupid mistakes. Do your work and check it.

16. mathstudent55

When you find an answer, check the answer. We get W = 9 ft and L = 11 ft Let's see if it makes sense. The area has to be 99 ft^2 A = LW = 11 ft * 9 ft = 99 ft^2 The length has to be 7 less than twice the width. L = 2w - 7 = 2(9) - 7 = 18 - 7 = 11 ft Yes, L = 11 ft and W = 9 ft make sense.

17. YanaSidlinskiy

Gotcha! Ok, makes sense!

18. YanaSidlinskiy

Thanks for the detailed explanations. I appreciate it!

19. mathstudent55

You are very welcome.