Диагонали AC и BD прямоугольника ABCD пере-секаются в точке O, BO=24, AB=45. Найдите AC.

Question 1

Задача Задача №281879

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Аноним

03 февраля 2024 06:09 · публичный вопрос

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Аноним 03 февраля 2024 06:09

Диагонали AC и BD прямоугольника ABCD пере-секаются в точке O, BO=24, AB=45. Найдите AC.

Answer

AC = 40 To find AC, we can use the property that the diagonals of a rectangle are congruent and bisect each other. Given that BO = 24 and AB = 45, we can apply the Pythagorean theorem to find AO and OB.

Using the equation: AO^2 + OB^2 = AB^2 we have: AO^2 + 24^2 = 45^2

Simplifying, we get: AO^2 + 576 = 2025 Subtracting 576 from both sides: AO^2 = 1449

Taking the square root of both sides: AO = √1449 ≈ 38.06

Since the diagonals bisect each other, we know that CO = AO = 38.06. Therefore, AC = 2CO = 238.06 = 76.12.

So, AC is approximately 76.12.

Question 2

Диагонали AC и BD прямоугольника ABCD пере-секаются в точке O, BO=24, AB=45. Найдите AC.

Answer

AC = 40 To find AC, we can use the property that the diagonals of a rectangle are congruent and bisect each other. Given that BO = 24 and AB = 45, we can apply the Pythagorean theorem to find AO and OB. Using the equation: AO^2 + OB^2 = AB^2 we have: AO^2 + 24^2 = 45^2 Simplifying, we get: AO^2 + 576 = 2025 Subtracting 576 from both sides: AO^2 = 1449 Taking the square root of both sides: AO = √1449 ≈ 38.06 Since the diagonals bisect each other, we know that CO = AO = 38.06. Therefore, AC = 2*CO = 2*38.06 = 76.12. So, AC is approximately 76.12.