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Properties of Triangles

Given a triangle with side lengths of 5, 12, and 14, is the largest angle in the triangle acute, right, or obtuse? Geometric knowledge helps us deduce much about triangles from limited information.

Triangles - Calculating Area


What is the area of the right triangle above with side lengths \(5, 12, \) and \(13\)?

In triangle \(ABC\) above, the lengths of some line segments are as follows: \[\begin{array} &BH=3, &CH=2, &AH=4. \end{array}\] What is the ratio of the area of \(\triangle ABH\) to the area of \(\triangle ACH?\)

In the above diagram, the area of \(\triangle ABD\) is \(25\) and the area of \(\triangle BCD\) is \(16.\) What is the ratio of the length of \(\overline{AD}\) to the length of \(\overline{DC}?\)

In the above diagram, \(a=10, b=8, c=6,\) and \(\angle CAB\) and \(\angle AHB\) are right angles. Find the value of \(x.\)

Hint: Find two different ways to represent the area (one using the legs and one using the hypotenuse) and set them equal.

What is the area of a triangle with side lengths 18, 24, and 30?


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