Question

BE - высота, AB=BC.Найдите BE, если AC=4√42 и AB=13

Answer 1

Ответ:

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Объяснение:

Answer 2

To find the value of BE, we can use the property of an isosceles triangle where AB = BC. We can start by applying the Pythagorean theorem to triangle ABC to find the length of AC:

AC^2 = AB^2 + BC^2 (4√42)^2 = 13^2 + BC^2 16 * 42 = 169 + BC^2 672 = 169 + BC^2 BC^2 = 672 - 169 BC^2 = 503

Now we know that BC^2 = 503. Since BC = BE + EC, we can substitute BC with BE + EC in the equation:

(BE + EC)^2 = 503

Expanding the equation, we have:

BE^2 + 2BE * EC + EC^2 = 503

Since AB = BC, we know that AB = 13, and EC = AB/2 = 13/2 = 6.5.

Substituting the values, we have:

BE^2 + 2BE * 6.5 + (6.5)^2 = 503

BE^2 + 13BE + 42.25 = 503

Rearranging the equation:

BE^2 + 13BE - 460.75 = 0

To solve this quadratic equation, we can use the quadratic formula:

BE = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 13, and c = -460.75. Substituting the values into the quadratic formula, we get:

BE = (-13 ± √(13^2 - 4 * 1 * -460.75)) / (2 * 1)

BE = (-13 ± √(169 + 1843)) / 2

BE = (-13 ± √2012) / 2

Now, we can calculate the value of BE:

BE = (-13 ± 44.874) / 2

BE ≈ (-13 + 44.874) / 2 or (-13 - 44.874) / 2

BE ≈ 31.874 / 2 or -57.874 / 2

BE ≈ 15.937 or -28.937

Since length cannot be negative, the value of BE is approximately 15.937.