+445 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 ____.
+2446 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:
Source: http://images.tutorvista.com/cms/images/113/altitude-of-triangle.png
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 \(4cm\).
