# 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

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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