In a right-angled triangle ABC, angle C = 90 degrees CD-height of the triangle
| July 14, 2021 | education
In a right-angled triangle ABC, angle C = 90 degrees CD-height of the triangle, AC = 5 cm, CB = 10 cm. What is the ratio of the areas of triangles ABC and CDB.
Determine the area of the triangle ABC.
Savs = CВ * AC / 2 = 10 * 5/2 = 25 cm2.
Let us calculate the length of the hypotenuse AB by the Pythagorean theorem.
AB ^ 2 = AC ^ 2 + CB ^ 2 = 25 + 100 = 125.
AB = 5 * √5 cm.
Let’s determine the coefficient of similarity of triangles.
AB / CB = 5 * √5 / 10 = √5 / 2.
The ratio of the areas of similar triangles is equal to the square of the similarity coefficient.
Savs / Ssvd = (√5 / 2) 2 = 5/4.
Answer: The area ratio is 5/4.
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