Question

triangles abc and def are similar triangles. solve. round to the nearest tenth.
find the area of triangle abc.
cm²
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Explanation:

Step1: Find the ratio of the sides

The ratio of the sides of \(\triangle ABC\) to \(\triangle DEF\) is \(\frac{AB}{DE}=\frac{30}{70}=\frac{3}{7}\)

Step2: Find the height of \(\triangle ABC\)

Since the triangles are similar, the ratio of their heights is the same as the ratio of their sides. Let the height of \(\triangle ABC\) be \(h\). Then \(\frac{h}{35}=\frac{3}{7}\), so \(h = 35\times\frac{3}{7}=15\)

Step3: Calculate the area of \(\triangle ABC\)

The area of a triangle is \(A=\frac{1}{2}\times base\times height\). For \(\triangle ABC\), base \(AB = 30\) and height \(h = 15\). So \(A=\frac{1}{2}\times30\times15=225\)

Answer:

\(225.0\)