Answer:
~1.5226
Step-by-step explanation:
You know that the area of a square or rectangle can be find by multiplying the base and height (sometimes referred to as length and width in 2 dimensions, but the idea is the same).
You are given that the lengths of two different sides of the rectangle are 3x + 2 and x. Therefore you can use the formula for area and the fact that you know the area to be 10 to solve for the value of x
(3x + 2) * (x) = 10
[tex]3x^2+2x[/tex] = 10 (You can distribute the x)
[tex]3x^2+2x[/tex][tex]- 10[/tex] = 0
Now here's the tricky part. You want to use the quadratic equation, which I have attached below as an image (note that a is the coefficient of x^2, b is the coefficient of x, and c is the constant. So in your case a = 3, b=2, and c=-10).
Plugging that in, you get:
[tex]\frac{-2 +/- \sqrt{2^2-4(3)(-10)}}{(2)(3)}[/tex] (note that I put +/- for the plus or minus sign)
Solving that equation, you should get x = ~-2.189 (when you subtract the square root) and x = ~1.5226 (when you add the square root). Since a negative length of a rectangle doesn't make sense, you find that x is equal to around 1.5226, which you can plug back in to confirm, if so desired.
