To solve for something like this, use the area of a triangle formula or A=1/2(b)(h) where A is the area, b is the base, and h is the height. Now that we have this, plug in the known values where x is the height:
24=1/2(x+2)(x)
Next, simplify the equation:
24=1/2(x^2+2x)
48=x^2+2x
Then, subtract over the 48 so that you are left with the quadratic:
x^2+2x-48=0
Since this is set to the value of 0, factor your quadratic. To factor, look for any two numbers that multiply to -48 and add to 2. These numbers would be -6 and 8. Then, you would write the quadratic as this:
(x-6)(x+8)=0
Then, set each factor to 0:
x-6=0
x+8=0
Then solve for the roots:
x=6
x=-8
Finally, remove the -8 value since you cannot have negative dimensions, and use x=6 to find your base and height. Since the base is two more than the height and the height is the x value, your height would be 2 and your base is 4.
