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# Math

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A triangle has an area of 12 cm2. If the length of one side of the triangle is 6 cm, then the altitude to that side is ____.

DerpofTheAbyss  Jun 2, 2017
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The altitude of a triangle is a line segment on a triangle that extends from a common vertex of two sides to the opposite side perpendicularly. This is a definition, but a picture is probably more helpful than a wordy, verbose definition. Here it is:

For the purposes of this problem, the altitude can be considered the same as the height of this triangle. Before attempting this problem, know the formula for the area of a triangle:

Let A=Area of triangle

Let b= base of the trangle

Let h= height, or altitude, of the triangle

$$A_\triangle=\frac{1}{2}bh$$

Substitute in the values that we know and solve for the unknown. In this particular problem, the total area is given, $$12cm^2$$.. This value would replace the A in the above formula. $$6cm$$ can replace b in the above formula, as this length is a base of this triangle. Now solve for the altitude:

 $$A_\triangle=\frac{1}{2}bh$$ As explained above, substitute the known values into the formula and solve for the unknown, the altitude. $$12=\frac{1}{2}*6h$$ Simplify $$\frac{1}{2}*6h$$ $$12=3h$$ Divide by 3 on both sides $$h=4cm$$ Of course, do not forget to attach the appropriate unit of measure to your final answer!

If the length of one side of the triangle is 6 cm, then the altitude to that side is $$4cm$$.

TheXSquaredFactor  Jun 2, 2017

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