Find the Area X | Important Geometry And Algebra Skills Explained

Find the Area X | Important Geometry And Algebra Skills Explained
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[@jeanmarcbonici9525]

Thank you for having taken care to calculate X in the general case where the triangle ABC is arbitrary (at least a priori). When the triangle ABC is right-angled at B, we show that there is only one such solution triangle for which AP=4 Sqrt(14/15), BP=2 Sqrt(42/5), BC=Sqrt (210) and therefore BQ=Sqrt(105/2) then PR=2 Sqrt(174/35) and CS=Sqrt(406/15), we note ABCr this unique right triangle solution. Any triangle ABC is solution if and only if it is the image of ABCr by a unimodular affine transformation Ta, i.e. an affine transformation for which vect(Ta) belongs to SL(2, R). For any solution triangle (not necessarily right-angled), we always have X=8 as you have shown.

[@احمدمحمد-ت8ط9ج]

تمرين جميل جيد .شرح واضح مرتب. تحياتنا لكم من غزة فلسطين شكرا جزيلا لكم والله يحفظكم ويحميكم ويرعاكم جميعا. تحياتنا لكم من غزة فلسطين .

[@MathBooster]

Thank you 🙂

[@akifbaysal9141]

Checked the end of video to verify my solution, same quadratic eq. and x=8.. Nice question to link all areas together and form an equation for a common x as + solution to all.. Thanks..

[@buff9943]

👍

[@idvbane8580]

V gd explain 🥰

[@MathBooster]

Thanks 😊

[@vijayannair2316]

V.nice

[@MathBooster]

Thanks 😊

[@8mice979]

i think it s easyer to use Menelaus Theorem!

[@MathBooster]

But the angle B is not given 90 degree.

[@idvbane8580]

Math is gd🥰🥰

[@epimaths]

Tìm góc❤❤❤

[@DB-lg5sq]

شكرا يمكن الاكتفاء بالمثلثينCAP وRAP للحصول على معادلة من الدرجة الثانية ذات المجهول x ومنه x=8

[@idvbane8580]

Geometry🥰🥰

[@idvbane8580]

Sir🥰🥰🥰

[@honestadministrator]

JOIN PQ , the median of ∆ PBC 27 - |∆ PQR | = |∆ PQR | + x + 7 |∆ PQR | = 10 - x/2 JOIN AC, AQ is median of ∆ABC x + 27 = |∆ ARC | + x + 7 |∆ ARC| = 20 Again PR / RC = | ∆ APR | / | ∆ ARC | PR / RC = | ∆ QPR | / | ∆ QRC | x / 20 = (10 - x/2 ) / (x + 7) x^2 + 7 x = 200 - 10 x x^2 + 17 x - 200 = 0 (x - 8) (x + 25) = 0 x = 8.

[@samarthchohan106]

Rq is not the height of triangle brq

[@MathBooster]

I have not taken RQ as height.

[@idvbane8580]

🥰🥰

[@idvbane8580]

Math🥰🥰

[@idvbane8580]

🥰🥰🥰