Ken is building a table. He attached planks of wood and now wants to build a border around the planks. The area of the entire table should be no larger than 3,276 square inches. All together, the planks are 36 inches wide and 72 inches long. Which quadratic equation represents the area of the planks and border combined? (The border must have equal width on each side.)

4x2 + 216x + 2,592 = 0

4x2 + 216x − 684 = 0

2x2 + 216x − 3,276 = 0

x2 + 108x + 3,276 = 0

Question

Ken is building a table. He attached planks of wood and now wants to build a border around the planks. The area of the entire table should be no larger than 3,276 square inches. All together, the planks are 36 inches wide and 72 inches long. Which quadratic equation represents the area of the planks and border combined? (The border must have equal width on each side.)  

4x2 + 216x + 2,592 = 0

4x2 + 216x − 684 = 0

2x2 + 216x − 3,276 = 0

x2 + 108x + 3,276 = 0

hartnn · Answer

borders will be on both sides, so the total dimensions will be 
36-2x and 72-2x
got this ? or should i draw and demonstrate ?

anonymous · Answer

Well, i fi understand correctly, those dimesnsions are for the plank and the border?

anonymous · Answer

@hartnn

hartnn · Answer

ok, yes. there should be 36+2x and 72+2x instead of what i wrote.
and yes.

anonymous · Answer

ok, so which one is for which?

anonymous · Answer

And, i understand, but which equation would it be?

hartnn · Answer

you need dimensions of entire table 
which is plank + border 
which is  36+2x and 72+2x

hartnn · Answer

now to get equation, use length * breadth = area

anonymous · Answer

what is breadth? you mean width?

hartnn · Answer

yes, i meant width

anonymous · Answer

so i multiply 36 by 2 and then 72 by 2? i'm not sure if i understand how to find the equation..

hartnn · Answer

length = 72+2x and width =72+2x
Area = 3276
so, 3276 =( 36+2x )( 72+2x)
got this ?

hartnn · Answer

***width = 36+2x

anonymous · Answer

yeah, im getting it. haha

hartnn · Answer

just simplify that now....
3276 =( 36+2x )( 72+2x)

anonymous · Answer

is it 3276=2592 + 4x^2??

hartnn · Answer

where did your 'x' term go ?? 
you'll also get 2 terms like 36* 2x + 72*2x

anonymous · Answer

my x term is 4x^2, i though..

anonymous · Answer

and what do you mean by youll also get two terms

hartnn · Answer

you have not distributed completely, 
( 36+2x )( 72+2x) will have 4 terms

anonymous · Answer

ohh, ok so 2592, 72x, 144x, and 4x^2

hartnn · Answer

yes, add all of them

anonymous · Answer

ok so it would be 2592, 216x, and 4x^2

anonymous · Answer

so its the first one

hartnn · Answer

yes, and don't forget 3276
4x^2+216x+2592 = 3276

hartnn · Answer

its not the first one....

anonymous · Answer

um, what you said sint even an option

anonymous · Answer

well, the first one is the only one with the correct terms in it

hartnn · Answer

because you still need to subtract 3276 from both sides! to get 0 on right side

anonymous · Answer

oh, so i just subtact it from 2592 than?

hartnn · Answer

yes

anonymous · Answer

it equals -684

hartnn · Answer

so, which option ?

anonymous · Answer

the second one!!

hartnn · Answer

you are $\huge \color{red}{\checkmark}$

anonymous · Answer

hahah yayy im so happy!! hah thank you!!

hartnn · Answer

welcome ^_^