You can use Stewart's theorem. But I didn't use it. I just assumed ABC to be an isosceles triangle. Split line BC into two right triangles of 9 length each, got a common height of 12 and worked out X from there. Done quicktime. But a nice little problem anyway.
15 Draw a perpendicular line BC to A to form three other triangles, ADP , ABP, and ACP, Since PD =5, and then AP = 12 (Pythagorean), Since PC = 9, , then x = 15 (since the triangle is a 3-4-5 scaled up by 3
I trinken this judgement is far to harsh. Sure, the method of explanation is repetitive and somewhat rigid. But I appreciate this. I do not like music or jokes in this kind of tutorials.
Method 3 using Stewart's theorem : b^2*m + c^2*n = a*(d^2 + m*n)
x^2*14 + x^2*4 = (14+4)*(13^2 + 14*4) ---> x^2 = 225 ---> x= 15
(14+4)/2=9 14-9=5
√[13^2-5^2]=√144=12
x=√[9^2+12^2]=√225=15
Construimos el triángulo isósceles interior de ados 13/13/(14-4=10)---> h²=13²-(10/2)²=144--->h=12---> X²=144+(5+4)²=225---> X=15.
Gracias y saludos.
(14)^2= 196A/O (13)^2= 169A/O (4)^2=16 A/O {196A/O+169A/O+16A/O}= 371A/O {60°A+60°B+60°C}=180°ABC /371A/O/180°ABC= 2.11 2.11^1 2.1^1 2.1 (ABC ➖ 2ABC+1).
You can use Stewart's theorem. But I didn't use it. I just assumed ABC to be an isosceles triangle. Split line BC into two right triangles of 9 length each, got a common height of 12 and worked out X from there. Done quicktime. But a nice little problem anyway.
14+4=9+9 , H=√(169-25)=√144=12,
АВ=√(144+81)=√225=15.
h=12 from one pytagorei, x=15 for second, nice but trivial
Basta usar o teorema de Stewart! 🎉
Se não me engano, essa questão já foi feita nesse canal.
Triangle ABD
Cos angle ADB
=(13^2+14^2-x^2)/2*13*14--(1)
In triangle ACD
Cos angle ADC =cos angle(180- ADB)
= - cos angle ADB
= (13^2+4^2-x^2)/2*13*4--(2)
From 1 & 2
(169+196 - x^2)/2*13*14
= - (169+ 16 - x ^2)/2*13*4
> (169+196 -x ^2)*4
=- 14(169+16-x^2)
>365*4 - 4x^2= 14x^2-2590
>18x^2 = 2590+1460
> x^2= 4050/18=225
x=15
Comment please
Method 3: Stewart Theorm!
13" = (14/18)•X" + (4/18)•X" - 14•4
169 = X" - 56 ↔️
X" = 169+56 = 225 ➡️
X = 15. Much-much Easier! 🤓
13^2=x^2-(4)(14)
169=x^2-56
x^2=169+56
So x=15.
Personally this can be done using only knowledge of Pythagorean triples and just that Method 1.
And I guessed x=15.
15
Draw a perpendicular line BC to A to form three other triangles, ADP , ABP, and ACP,
Since PD =5, and then AP = 12 (Pythagorean), Since PC = 9, , then x = 15 (since the triangle is a 3-4-5 scaled up by 3
x = 15
I did it in my head. 15
Too much calculation in 2nd method. Inefficient for this question, but good application of Cosine Rule.
好麻烦。勾股定理用两次，俄罗斯套娃。Simple is best
Appreciate your sharing of knowledge but the way you do it is boring due to the way you explain. Please level up. Thanks.
I trinken this judgement is far to harsh. Sure, the method of explanation is repetitive and somewhat rigid. But I appreciate this. I do not like music or jokes in this kind of tutorials.
x=15