Devin wants to have equal amounts of room on all four sides of his ping pong table. A 5ft by 9ft table is placed in the center of a rectangular room that has an area of 221 square feet. What is the width of the clear space Devin will have on all sides of his table?

How do I solve this?

Question

Devin wants to have equal amounts of room on all four sides of his ping pong table. A 5ft by 9ft table is placed in the center of a rectangular room that has an area of 221 square feet. What is the width of the clear space Devin will have on all sides of his table?

How do I solve this?

anonymous · Answer

find the area of the table  (45) subtract from full area = 221
221-45 = 176

to determine the width  only ....

anonymous · Answer

176/4 = 44 ft

anonymous · Answer

I need to use the completing the square method or something; I already tried to logic my way out of it like that. My teacher wouldn't accept that answer.

anonymous · Answer

If by "room" we mean distance, and assume the room has the same proportions as the table, we end up with something like$$(5+2x)(9+2x)=221\rightarrow 4x^2+28x+45=221\rightarrow 4x^2+28x-176=0$$

anonymous · Answer

I'm not sure this question is very well posed.

anonymous · Answer

Your answer is good, i think, AnimalAin. I think that's how I'm supposed to solve it. My teacher didn't givem e a whole lot of practice on these types of problems -- I haven't run into them more than once or twice before.

anonymous · Answer

Continuing....$$4(x^2+7x-44)=0\rightarrow (x+11)(x-4)=0\rightarrow x=4$$

anonymous · Answer

Check step:  dimension of the room would be 17 by 13, with area 221

anonymous · Answer

...and he needs to tear out an end wall to extend the room at least another ten feet to be able to play table tennis.....