In triangle ABC, the area of which is 35 cm squared on the extension of the side AC
| May 14, 2021 | education
In triangle ABC, the area of which is 35 cm squared on the extension of the side AC, point M is chosen so that CM = 3 \ 5 AC. Find the area of triangle ABM.
Let’s draw the height BH, which is the same for triangles ABC and ABM.
The area of the triangle ABC = AC * BH / 2 = 35 cm2.
AC * BH = 70 cm2.
Since CM = 3 * AC / 5, then AM = AC + 3 * AC / 5 = 8 * AC / 5.
The area of the triangle ABM = AM * BH / 2 = (8 * AC / 5) * BH / 2 = (8/5) * AC * BH / 2 = (8/5) * 70/2 = 56 cm2.
Answer: The area of the triangle is 56 cm2.
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