ﻓﻲ ﺍﻟﻤﺮﺑﻊ ABCD ﺇﺫﺍ ﻛﺎﻥ AC=16 ، AE=3x-1 ﻓﺈﻥ ﻗﻴﻤﺔ x ؟
نوفر لكم في موقع الافق حل السؤال ﻓﻲ ﺍﻟﻤﺮﺑﻊ ABCD ﺇﺫﺍ ﻛﺎﻥ AC=16 ، AE=3x-1 ﻓﺈﻥ ﻗﻴﻤﺔ x بيت العلم، يعتبر هذا السؤال أحد الأسئلة المهمة الذي يتم تكرارها في واجبات منصة مدرستي و الواجبات المدرسية المنزلية والاختبارات.
ﻓﻲ ﺍﻟﻤﺮﺑﻊ ABCD ﺇﺫﺍ ﻛﺎﻥ AC=16 ، AE=3x-1 ﻓﺈﻥ ﻗﻴﻤﺔ x
في موقع "الافـق" التعليمي نسعى لتوفير إجابات صحيحة وشاملة للأسئلة والواجبات المدرسية، بهدف مساعدتهم في تحقيق الدرجة الكاملة. نقدم الحلول بشكل مختصر وواضح، مع التركيز على سهولة فهم الخطوات الصحيحة. بما في ذلك حل السؤال التالي:
ﻓﻲ ﺍﻟﻤﺮﺑﻊ ABCD ﺇﺫﺍ ﻛﺎﻥ AC=16 ، AE=3x-1 ﻓﺈﻥ ﻗﻴﻤﺔ x؟
الـجـواب :
3.
ﻓﻲ ﺍﻟﻤﺮﺑﻊ ABCD ﺇﺫﺍ ﻛﺎﻥ AC=16 ، AE=3x-1 ﻓﺈﻥ ﻗﻴﻤﺔ x / الشرح والتوضيح
It seems like you are asking for the value of x in the figure ABCD, where AC is 16 and AE is 3x-1. To find the value of x, we can use the fact that AE is a segment on the line connecting points A and E.
Since AC is a diagonal of the rectangle ABCD, it separates the rectangle into two congruent right triangles. Let's call the length of AB (or the height of the rectangle) as h and the length of BC (or the width of the rectangle) as w.
Now, let's focus on one of the right triangles, specifically triangle AEC. According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of its hypotenuse.
In this case, AE is one of the legs, AC is the hypotenuse, and EC is the other leg. So we have the equation: AE^2 + EC^2 = AC^2
Substituting the known values, we get: (3x-1)^2 + EC^2 = 16^2
Expanding and simplifying the equation: 9x^2 - 6x + 1 + EC^2 = 256
Since ABCD is a rectangle, EC is equal to AB, which is h. So we have: 9x^2 - 6x + 1 + h^2 = 256
Since h is not given in the question, we cannot find the exact value of x with the information provided. We would need to know either the value of h or another relationship between h and x in order to solve for x.
