Answer:
length- 10cm, width- 5cm
Explanation:
You want to convert this into an algebraic equation.
Since a=lw, in this case, 50=lw. Subbing (x+3) for l and (x-2) for w, we get the equation (x+3)(x-2)=50.
Using FOIL, we can expand the brackets to make x²-2x+3x-6=50 and collect like terms to x²+x-6=50.
We want all the numbers on one side (to use the null factor law), so we subtract 50 from both sides. This gives x²+x-56=0.
From there, we factorise it, which becomes (x-7)(x+8)=0. (I used the cross method for this)
With the null factor law, one of the brackets must be equal to 0, meaning x-7=0 or x+8=0. This gives x as either 7 or -8.
With measurement, units must be positive, meaning it has to be 7. We can sub this for x in the 2 equations (length and width) to get the answers.
Length=x+3 becomes 7+3, which is 10cm.
Width=x-2 becomes 7-2, which is 5cm.
**This content involves writing, expanding, and factorising quadratic equations, and the null factor law which you may wish to revise. I'm always happy to help!