Question

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

Explanation:

Step1: Recall area - formula for triangle

The area of a triangle can be calculated using the formula $A=\frac{1}{2}ab\sin C$ (where $a$ and $b$ are two - side lengths of the triangle and $C$ is the included angle between them). For $\triangle ABC$, we only know the side - lengths $AB = 4$, $BC = 6$, and $AC = 7$, but we don't know any of the angles. So, we can't calculate its area directly.

Step2: Analyze $\triangle XYZ$

For $\triangle XYZ$, we know $XY = 2$, $YZ = 12$, and the included angle $\angle Y=98^{\circ}$. Using the formula $A=\frac{1}{2}ab\sin C$, we have $A_{XYZ}=\frac{1}{2}\times XY\times YZ\times\sin Y=\frac{1}{2}\times2\times12\times\sin98^{\circ}= 12\sin98^{\circ}\approx12\times0.9903 = 11.8836$. But we still can't compare it with the area of $\triangle ABC$ since we don't know the area of $\triangle ABC$.

Answer:

More information is needed to compare