Question

Can someone please check over my answer and explain to me if I did something wrong thank you very much
Kim wants to have equal amounts of room on all four sides of her dining room table. A 5ft by 8ft table is placed in the center of a rectangular room that has an area of 154 square feet. What is the width of the clear space Kim will have on all sides of her table?
answer: length of room =8+2x
width =5+2x
(8+2x)(5+2x)=154
40+10x+16x+4x^2=154
4x^2+26x-114=0
2x^2+13x-57=0
2x^2-6x+19x-57= 0
2x(x-3)+19(x-3)=0
(2x+19)(x-3)=0
x=-19/2 OR 3
x=3ft
my teacher told me I was wrong

Answer 1

this lesson is based off quadratic equations so did I not follow the rules of a quadratic equation I just want to learn from my mistake

Answer 2

I would really appreciate it if you could help me I'm not asking for a answer I just would like to know what I did wrong because my teacher wants to talk about it tomorrow and i'm nervous cause idk what I did that she is saying is wrong

Answer 3

(8+2x) * (5 + 2x) = 154
4x^2 + 26x + 40 = 154
2x^2 + 13x - 57 = 0
2x^2 - 6x + 19x - 57 = 0
2x(x - 3) + 19(x - 3) = 0
(2x + 19)(x - 3) = 0
x = 3 or -9.5

I am also getting 3 feet width.

Let us put back in the original problem. 5' x 8' table
room dimensions: 5 + 3 + 3 = 11' by 8 + 3 + 3 = 14
14 x 11 = 154 square feet.

Answer 4

so the right answer would be 154 square feet? maybe that's why she told me i'm wrong I don't know that makes me so nervous! But thank you for at least comforting me by getting the same answer and somewhat explaining

Answer 5

No. 154 square feet is given in the problem. I just verified that an equal gap of 3 feet on all sides of the table gives us the room dimension 14 x 11 which satisfies the area of the room given in the problem as well as the condition that there be equal space on all four sides of the table. So the 3 feet width is correct.

But if they asked for the room dimension then you will have to say 14 feet x 11 feet.

But if they wanted the width 3 feet is the correct answer.

Answer 6

Oh Okay i'm sorry that was stupid of me algebra is very hard for me and I get quite confused that makes a lot more sense and you solved it like a quadratic equation right? so everything is correct at least I can explain it to her now I really appreciate it

Answer 7

Maybe they wanted the sum of ALL widths in which case 4 * 3 = 12 feet will be the correct answer.

Answer 8

maybe(: I will keep that in mind to tell her just in case thank you!

Answer 9

But your math is correct. And the width = 3 is correct.