Answer:
x+4 square meters
Step-by-step explanation:
In general, when we have two expressions
and
:
![(x+a)(x+b)=x^2+(a+b)x+ab](https://tex.z-dn.net/?f=%28x%2Ba%29%28x%2Bb%29%3Dx%5E2%2B%28a%2Bb%29x%2Bab)
In words, the coefficent of the middle term is the <em>sum</em> of a and b, and the last term is the <em>product</em> of a and b. In our given expression:
![a+b=13\\ab=36](https://tex.z-dn.net/?f=a%2Bb%3D13%5C%5Cab%3D36)
Thankfully, we're already given one of these terms:
. Solving for b in that first equation, we get
![9+b=13\\b=4](https://tex.z-dn.net/?f=9%2Bb%3D13%5C%5Cb%3D4)
9 × 4 is 36, so this result checks out! So, with a length of
meters, our width must be
meters.