Q : in AB^Δ C : A = 90^o and , m_( b) ^2 + m_( c) ^( 2) = 100. find the value of ” a ” . note : ⟨ m_( a) := the median corresponding to ” A ” . −−− m.n−−−


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 176100 by mnjuly1970 last updated on 12/Sep/22

$Q :$ $i n A \overset{Δ}{B C} : A = 90^{o} a n d, m_{b}^{2} + m_{c}^{2} = 100 .$ $f i n d t h e v a l u e o f^{″} a^{″} .$ $n o t e : ⟨ m_{a} := t h e m e d i a n c o r r e s p o n d i n g t o^{″} A^{″} .$ $- - - m . n - - -$
	Answered by Rasheed.Sindhi last updated on 12/Sep/22
	$• a^2 =b^2 +c^2 • b^2 +((c/2))^2 =m_c ^2 • c^2 +((b/2))^2 =m_b ^2 m_( b) ^2 + m_( c) ^( 2) ={c^2 +((b/2))^2 }+{b^2 +((c/2))^2 }=100 c^2 +(b^2 /4)+b^2 +(c^2 /4)=100 5b^2 +5c^2 =400 b^2 +c^2 =80 a^2 =80 a=(√(80)) =4(√5)$
	$∙ a^{2} = b^{2} + c^{2}$ $∙ b^{2} + {(\frac{c}{2})}^{2} = m_{c}^{2}$ $∙ c^{2} + {(\frac{b}{2})}^{2} = m_{b}^{2}$ $m_{b}^{2} + m_{c}^{2}$ $= {c^{2} + {(\frac{b}{2})}^{2}} + {b^{2} + {(\frac{c}{2})}^{2}} = 100$ $c^{2} + \frac{b^{2}}{4} + b^{2} + \frac{c^{2}}{4} = 100$ $5 b^{2} + 5 c^{2} = 400$ $b^{2} + c^{2} = 80$ $a^{2} = 80$ $a = \sqrt{80} = 4 \sqrt{5}$
	Commented by mnjuly1970 last updated on 12/Sep/22

	$g r a t e f u l s i r r a s h e e d$
	Answered by behi834171 last updated on 13/Sep/22

	$2 m_{b} = a^{2} + c^{2} - \frac{b^{2}}{2}$ $2 m_{c} = a^{2} + b^{2} - \frac{c^{2}}{2} \Rightarrow 2 (m_{b}^{2} + m_{c}^{2}) = 2 a^{2} + \frac{a^{2}}{2} \Rightarrow$ $m_{b}^{2} + m_{c}^{2} = \frac{5 a^{2}}{4} = 5 {(\frac{a}{2})}^{2} = 5 m_{a}^{2}$ $\Rightarrow 200 = \frac{5 a^{2}}{2} \Rightarrow a = \sqrt{80} = 4 \sqrt{5} . ◼$
	Commented by mnjuly1970 last updated on 13/Sep/22

	$m a m n o o n o s t a d$
	Commented by behi834171 last updated on 13/Sep/22

	$[n o t e :$ $w h e n : ∡ A = 90^{∙} \Rightarrow m_{a} = \frac{a}{2}, m_{b}^{2} + m_{c}^{2} = 5 m_{a}^{2}$ $\Rightarrow m_{a}^{2} = \frac{m_{b}^{2} + m_{c}^{2}}{5} = \frac{100}{5} = 20$ $\Rightarrow m_{a} = 2 \sqrt{5} \Rightarrow a = 2 m_{a} = 4 \sqrt{5} .]$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum