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21 August, 23:49

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.

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  1. 22 August, 03:40
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    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.
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