Question

which statement is true of the right triangles abc and def? area of abc is less than area of def. there is not enough information to compare the areas of triangles abc and def. area of abc is greater than area of def. area of abc is equal to the area of def.

Explanation:

Step1: Calculate area of triangle ABC

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). For \(\triangle ABC\), base \(AC = 10\) units and height \(AB=6\) units.

$$A_{ABC}=\frac{1}{2}\times10\times6 = 30$$

Step2: Calculate area of triangle DEF

For \(\triangle DEF\), base \(EF = 6\) units and height \(DF = 10\) units.

$$A_{DEF}=\frac{1}{2}\times6\times10=30$$

Answer:

Area of \(ABC\) is equal to the area of \(DEF\).