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.