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

Question

yanasidlinskiy · Answer

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

mathstudent55 · Answer

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

mathstudent55 · Answer

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

yanasidlinskiy · Answer

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?

mathstudent55 · Answer

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.

mathstudent55 · Answer

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

yanasidlinskiy · Answer

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

mathstudent55 · Answer

No problem. Take your time.

yanasidlinskiy · Answer

I got 22.

mathstudent55 · Answer

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

yanasidlinskiy · Answer

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

mathstudent55 · Answer

$\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   $\large w = -5.5$

mathstudent55 · Answer

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

yanasidlinskiy · Answer

It's the minor stuff that kills me lol.

mathstudent55 · Answer

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

mathstudent55 · Answer

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.

yanasidlinskiy · Answer

Gotcha! Ok, makes sense!

yanasidlinskiy · Answer

Thanks for the detailed explanations. I appreciate it!

mathstudent55 · Answer

You are very welcome.