Question 1002096: I have been stuck to this question on my math exam..can you solve this for me?
Find the dimension of a rectangle with an area of 27 square meters, if the length of a rectangle is three more than twice the width.
Found 2 solutions by Theo, Cromlix:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! area of a rectangle = length * width
the length is equal to 3 more than twice the width.
the equation for that is:
length = 2 * width + 3
start with:
area = length * width
replace length with 2 * width + 3 to get:
area = (2 * width + 3) * width
simplify this to get:
area = 2 * width^2 + 3 * width
since the area = 27, then replace area with 27 to get:
27 = 2 * width^2 + 3 * width
subtract 27 from both sides of this equation to get:
0 = 2 * width^2 + 3 * width - 27
this is the same aqs:
2 * width^2 + 3 * width - 27 = 0
this equation is in standard form of ax^2 + bx + c = 0.
replace width with x and your equation becomes:
2x^2 + 3x - 27 = 0
now it's easier to see that your equation is in the standard form of ax^2 + bx + c = 0
since it is in standard form, you can find a and b and c.
a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.
in your equation of 2x^2 + 3x - 27 = 0, you get:
a = 2
b = 3
c = -27
don't forget that you made x = width.
you will need that fact later on.
to factor the equation of 2x^2 + 3x - 27 = 0, use the quadratic formula.
the quadratic formula says that:
x = (-b + or - sqrt(b^2-4ac)) / (2a)
this results in 2 possible answers.
x = (-b + sqrt(b^2-4ac))/(2a) or:
x = (-b - sqrt(b^2-4ac))/(2a)
when a = 2 and b = 3 and c = -27, you get:
b^2 = 3^2 = 9
4ac = 4*2*-27) = -216
b^2-4ac = 9-(-216) = 9+216 = 225
sqrt(b^2-4ac) = sqrt(225) = 15
-b = -3
2a = 4
x = (-b + sqrt(b^2-4ac))/(2a) or:
x = (-b - sqrt(b^2-4ac))/(2a) becomes:
x = (-3 + 15)/4 or:
x = (-4 - 15)/4 which becomes:
x = 3 or:
x = -4.5
since x can't be negative, you are left with:
x = 3
now's the time to remember that x represents the width.
go back to your original equation that said:
27 = length * width
since width = 3, this equation becomes 27 = length * 3
solve for length to get length = 9.
you have length = 9 and width = 3
now's the time to confirm your solution satisfies the problem requirements.
those are:
Find the dimension of a rectangle with an area of 27 square meters, if the length of a rectangle is three more than twice the width.
you found the dimensions.
they are length = 9 and width = 3.
an additional requirement is that length is equal to three more than twice the width.
the width is 3.
twice the width is 6
length is 9 which is 3 more than 6.
length is 3 more than twice the width so you have met that requirement.
you're solution is good.
the dimensions are:
length = 9
width = 3
Answer by Cromlix(4381)  (Show Source):
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