The length of a rectangular frame is represented by the expression 2x + 8, and the width of the rectangular frame is represented by the expression 2x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 160 square inches.

4x2 + 32x + 48 = 0
4x2 + 28x − 112 = 0
2x2 + 32x − 112 = 0
x2 + 12x + 48 = 0

Question

The length of a rectangular frame is represented by the expression 2x + 8, and the width of the rectangular frame is represented by the expression 2x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 160 square inches.

4x2 + 32x + 48 = 0
 4x2 + 28x − 112 = 0
 2x2 + 32x − 112 = 0
 x2 + 12x + 48 = 0

darkknight · Answer

so do you know the formula for the area of a rectangle?

Isamay0916 · Answer

yes

Isamay0916 · Answer

A= wl

darkknight · Answer

So area is length times width
we are given that the length is  2x+8 and the width is 2x+6

darkknight · Answer

So that means that 2x+8)(2x+6) = 160

darkknight · Answer

Do you know how to factor?

Isamay0916 · Answer

yes i do

darkknight · Answer

so to solve this, we will use foil. 2x+8)(2x+6

ramen · Answer

yes so just first multiply the terms together foil

Isamay0916 · Answer

ok ty

darkknight · Answer

which is 4x^2+16x+12x+48
which is 4x^2+28x+48

ramen · Answer

this is not one of the solutions darkknight

ramen · Answer

this is an example of a mistake that we can commonly make, so lets try and find the error he made

darkknight · Answer

Are you sure the answer choices are right @Isamay0916

Isamay0916 · Answer

yes let me copy them down again.

ramen · Answer

ok actually you may have maybe switched one of the numbers

Isamay0916 · Answer

The length of a rectangular frame is represented by the expression 2x + 8, and the width of the rectangular frame is represented by the expression 2x + 6. Write an equation to solve for the width of a rectangular frame that has a total area of 160 square inches.

4x2 + 32x + 48 = 0
 4x2 + 28x − 112 = 0
 2x2 + 32x − 112 = 0
 x2 + 12x + 48 = 0

darkknight · Answer

Did you copy the question right?

Isamay0916 · Answer

yes i did

ramen · Answer

well the answer is definitely supposed to be 4x^2+28x+48 but it doesn't seem like   the solutions are right

Isamay0916 · Answer

hmm thats strange

ramen · Answer

yes it really is..

Isamay0916 · Answer

oh well thank you for helping me

Isamay0916 · Answer

@darkknight @ramen

darkknight · Answer

no we are probebly doing something wrong

darkknight · Answer

hold on

ramen · Answer

i feel it too

Isamay0916 · Answer

ok

darkknight · Answer

Got an idea
So we have 4x^2+28x+48 but that is equal to 160
subtract 160 and you have
4x^2+28x-112

darkknight · Answer

That is your answer

darkknight · Answer

I am the darkknight

Isamay0916 · Answer

haha thank you darkknight!

ramen · Answer

THATS WHAT I SAID DARKKNIGHT BUT YOU SAID I WAS WRONG

ramen · Answer

mmmm lmao

Isamay0916 · Answer

lol

darkknight · Answer

@ramen, where?

ramen · Answer

aww shoot i deleted it bc i thought it was wrong

Isamay0916 · Answer

Was it this one "well the answer is definitely supposed to be 4x^2+28x+48 but it doesn't seem like   the solutions are right"

darkknight · Answer

okay ramen. I didn't see that answer

ramen · Answer

yes because you werent paying attention but ok.

Isamay0916 · Answer

Okay, okay, both of you found the answer and ty

darkknight · Answer

yw

ramen · Answer

yw good job