SOLUTION: This is an Area Problem. The directions say:Find the dimensions of the rectangle or triangle that has the given area. number 44, the area is 34 square meters. the length of the r

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is an Area Problem. The directions say:Find the dimensions of the rectangle or triangle that has the given area. number 44, the area is 34 square meters. the length of the r      Log On


   

Question 189239This question is from textbook McDougal Littel Algebra 1
: This is an Area Problem.
The directions say:Find the dimensions of the rectangle or triangle that has the given area.
number 44, the area is 34 square meters. the length of the rectangle is (X+11)m and the width is (X-4). I cannot figure out how to start the problem.
THIS IS URGENT SO CAN YOU PLEASE GET BACK TO ME BEFORE TONIGHT. This question is from textbook McDougal Littel Algebra 1

Found 2 solutions by jim_thompson5910, jonvaliente:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Because "the area is 34 square meters", this tells us that A=34


Since the "length of the rectangle is (X+11)m", this means that L=x%2B11


Also, since "the width is (X-4)", this means that W=x-4


A=LW Start with the area of a rectangle formula


34=%28x%2B11%29%28x-4%29 Plug in A=34, L=x%2B11 and W=x-4


34=x%5E2-4x%2B11x-44 FOIL


0=x%5E2-4x%2B11x-44-34 Subtract 34 from both sides.


0=x%5E2%2B7x-78 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=7, and c=-78


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%281%29%28-78%29+%29%29%2F%282%281%29%29 Plug in a=1, b=7, and c=-78


x+=+%28-7+%2B-+sqrt%28+49-4%281%29%28-78%29+%29%29%2F%282%281%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--312+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-78%29 to get -312


x+=+%28-7+%2B-+sqrt%28+49%2B312+%29%29%2F%282%281%29%29 Rewrite sqrt%2849--312%29 as sqrt%2849%2B312%29


x+=+%28-7+%2B-+sqrt%28+361+%29%29%2F%282%281%29%29 Add 49 to 312 to get 361


x+=+%28-7+%2B-+sqrt%28+361+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-7+%2B-+19%29%2F%282%29 Take the square root of 361 to get 19.


x+=+%28-7+%2B+19%29%2F%282%29 or x+=+%28-7+-+19%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29 or x+=++%28-26%29%2F%282%29 Combine like terms.


x+=+6 or x+=+-13 Simplify.


So the possible answers are x+=+6 or x+=+-13

However, if we plug in x+=+-13 into either L=x%2B11 or W=x-4, we get

L=x%2B11=-13%2B11=-2 ... W=x-4=-13-4=-17


Since a negative length or width doesn't make any sense, we must discard this possible solution


So the only solution for "x" is x+=+6


This means that the length and width are:

Length: L=x%2B11=6%2B11=17

Width: W=x-4=6-4=2


So the length is 17 meters and the width is 2 meters.

Answer by jonvaliente(64) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is given by the product of its length and width. So from this, we get an equation:
(x+11)*(x-4)=34
Using FOIL we get:
x%5E2%2B7x-44=34
Subtracting 34 from both sides, we get:
x%5E2%2B7x-78=0
Factoring this quadratic equation, we get:
%28x%2B13%29%28x-6%29=0
x+13=0 and/or x-6=0
x=-13 and/or x=6
If x=-13, then the length of the rectangle, (x+11)=(-13)+11=-2. But length cannot be negative, so we take x=6
where (x+11)=(6+11)=17=length of the rectangle
(x-4)=6-4=2=width of the rectangle
So you now have a rectangle with dimensions 17m x 2m
Hope this helps.