Question

comparing areas of triangles which statement about the relative areas of △abc and △xyz is true? more information is needed to compare. the area of △abc > the area of △xyz. the area of △abc < the area of △xyz.

Explanation:

Step1: Recall area - formula for triangles

The area of a triangle can be calculated in different ways. For a triangle with two - side lengths \(a\) and \(b\) and the included - angle \(\theta\), the area formula is \(A=\frac{1}{2}ab\sin\theta\). For \(\triangle ABC\), if we assume the sides are \(a = 4\), \(b = 6\), and we don't know the included - angle. The area \(A_{ABC}=\frac{1}{2}\times4\times6\times\sin\angle BAC\). For \(\triangle XYZ\), with \(a = 2\), \(b = 12\), and \(\theta = 98^{\circ}\), the area \(A_{XYZ}=\frac{1}{2}\times2\times12\times\sin98^{\circ}\).

Step2: Calculate the areas

\(A_{ABC}=12\sin\angle BAC\) and \(A_{XYZ}=12\sin98^{\circ}\). Since \(\sin98^{\circ}\approx0.9903\), but we don't know the value of \(\sin\angle BAC\). It could be any value between \(0\) and \(1\).

Answer:

More information is needed to compare.