The area of a rectangular garden is given by the trinomial #x^2+6x-27#. What are the possible dimensions of the rectangle?

2 Answers
May 16, 2018

#x=3, -6#

Explanation:

This needs to be double checked but I'm guessing you just solve the quadratic formula to find values for #x# and it's as simple as that.

If so, then all you do is factorise and solve, factorising a quadratic involves two rules the numbers in the brackets have to sum to make #b# and multiply to make #c# of the formula #ax^2+bx+c#

9 and -3 multiply to make -27 and add to make 6 therefore

#(x-3)(x+6)#

since this is a quadratic and equals zero that tells you that either one of the brackets are equal to zero (as anything multiplied by zero is zero)

#x-3=0 therefore x=3#
#x+6 = 0 therefore x=-6#

May 16, 2018

#A=lw=x^2+6x-27# so the dimensions are #l times w# with any #l>0# and

#w=A/l={x^2+6x-27}/l.#

Explanation:

This is probably just supposed to be a question about factoring:

# A = x^2 + 6 x - 27 = (x + 9)(x - 3)#

But the factors don't really constrain the rectangle so this isn't a very good question.