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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. See more

As shown in the above diagram, Raj folds a rectangular paper \(ABCD\) in such a way that side \(BC\) becomes \(BE.\) If the length of \(\overline{AB}\) is \(3\) and the length of \(\overline{BC}\) is \(15,\) what is the area of \(\triangle ABF?\)

**Note:** The above diagram is not drawn to scale.

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In the above diagram, we are given \[\angle BAC=90^\circ, \angle ACD=75^\circ, \angle CBD=75^\circ, \angle BDE=110^\circ.\] What is \(\angle ABC\) in degrees?

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In the above diagram, the ratio of the length of \(\overline{AD}\) to the length of \(\overline{DC}\) is \(3:2.\) If the area of \(\triangle ABE\) is \(13,\) what is the area of \(\triangle BEC ?\)

**Note:** The above diagram is not drawn to scale.

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