# In triangles ABC and NML, the heights CE and NH are plotted. It is known that CE = NH, and the AB side is 6 times larger

August 18, 2021 | education

| **In triangles ABC and NML, the heights CE and NH are plotted. It is known that CE = NH, and the AB side is 6 times larger than the ML side. The area of triangle NML is 8. Find the area of triangle ABC.**

The area of a triangle is found by the formula:

S = 1/2 * a * h.

Let’s write the area formula for our triangles:

S (Δ NML) = 1/2 * ML * NH = 8.

S (Δ ABC) = 1/2 * AB * CE.

By the condition NH = CE, AB = 6ML, we substitute this into the formula for the area of the triangle ABC.

S (Δ ABC) = 1/2 * 6ML * NH = 6 * S (Δ NML) = 6 * 8 = 48.

Answer: The area of triangle ABC is 48.

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