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 triangle - area formula

The area of a triangle can be calculated by \(A=\frac{1}{2}ab\sin C\) (where \(a\) and \(b\) are two - side lengths and \(C\) is the included angle). For \(\triangle ABC\), let \(a = 4\), \(b = 7\), but the included angle is unknown. For \(\triangle XYZ\), \(a = 2\), \(b = 12\), and the included angle \(C = 30^{\circ}\), so \(A_{XYZ}=\frac{1}{2}\times2\times12\times\sin30^{\circ}\).

Step2: Calculate area of \(\triangle XYZ\)

We know that \(\sin30^{\circ}=\frac{1}{2}\), so \(A_{XYZ}=\frac{1}{2}\times2\times12\times\frac{1}{2}=6\).

Step3: Analyze \(\triangle ABC\)

Since the included - angle of the sides with lengths 4 and 7 in \(\triangle ABC\) is unknown, we cannot calculate its area.

Answer:

More information is needed to compare.