In a right-angled triangle ABC, the angle ABC = 90 degrees, BC = 16 cm, AC = 20 cm. Points P and T are the middle

| January 29, 2021 | education

In a right-angled triangle ABC, the angle ABC = 90 degrees, BC = 16 cm, AC = 20 cm. Points P and T are the middle of the sides BC and AC, respectively. Calculate the area of the TРС triangle.

To solve the problem, we will use the property of the middle line of a triangle, which cuts off a triangle similar to the original. The area of such a triangle is four times less than the area of the original triangle.
In the triangle ABC we find the leg AB and the area of the triangle ABC.
AB = √ (AC² – BC²) = √ (400 – 256) = √144 = 12 (cm).
S ABC = 1/2 * AB * BC = 1/2 * 12 * 16 = 96 (cm²).
The area of the original triangle is known, we find the area of the TPC triangle:
S TPC = 1/4 * S ABC = 1/4 * 96 = 24 (cm²).
Answer: The area of a TPC triangle is 24 cm².



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