Question

The length of the top of the table is 3 m greater than the width. The area is 88m^2. Find the dimensions of the table.

Answer 1

The area of a rectangle is found using the formula A=LW. You need to express the length and width of this table using one variable. Since the length is described in terms of the width, let's call the width w. The length is 3m more than the width, so we can call the length w+3. Put these expressions of the length and width into the formula: 
A=LW, A=88m², L= (w+3), w=w substitute: 
88=w(w+3) (ok I did WL instead of LW but it's the same thing) Distribute the w: 
88 = w²+3w subtract 88 from each side 
0 = w²+3w-88 factor. w^2 can only be factored by w*w so set that up: 
(w )(w ). Now look at the last term, it is -88. You need to find two factors of -88, and since factors multiply to get the number, you must have one positive and one negative factor to get -88, so go ahead and put them into your parentheses: 
(w+ )(w- ). Now find factors of -88 that when added together give you 3, the coefficient of the middle term. -8 and 11 add up to 3, so put those into your factors: 
(w+11)(w-8) and remember that this equals 0: 
(w+11)(w-8)=0 Now when you multiply two numbers and get a product of 0, at least one of those numbers must equal 0 since any number times 0 equals 0. Either one can be 0, so set each equal to 0: 
w+11=0 subtract 11 from each side 
w= -11 

w-8=0 add 8 to each side 
w=8 

Now you're asked to give the length and width of the table top. The table can't have a dimension that is negative, so we can discard the solution w= -11. We find that the width of the table is 8 feet. To find the length, go back to how we expressed the length, 3 more than the width: 
L=3+w, w=8 substitute 
L=3+8 add 
L=11. 

So the length of your table top is 11m and the width is 8m.