A triangle has an area of 24 square inches, and its base is 2 inches more than its height. Find the base and height of the triangle.

The base of the triangle is () inches and the height is () inches.

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.