Math Question and Answers


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 184718 by sonukgindia last updated on 10/Jan/23

	Answered by HeferH last updated on 10/Jan/23

	$L e t 2 a b e t h e s i d e o f t h o s e s q u a r e s a n d x t h e$ $l a r g e r s i d e o f t h e y e l l o w t r i a n g l e .$ $A_{r e c t} = 2 a \cdot 4 a = 8 a^{2}$ $b y p r o d u c t o f c h o r d s :$ $a \sqrt{5} \cdot x = a^{2}$ $x = \frac{a}{\sqrt{5}}$ $t h e y e l l o w t r i a n g l e i s a s p e c i a l o n e k, 2 k, k \sqrt{5}$ $f r o m t h i s w e g e t t h e h e i g h t a n d t h e b a s e .$ $A_{△} = {(\frac{2 a}{5})}^{2} \cdot \frac{1}{2} = \frac{2 a^{2}}{25} \Rightarrow$ $\frac{A_{△}}{A_{r e c t}} = \frac{2 a^{2}}{25} \cdot \frac{1}{8 a^{2}} = \frac{1}{100}$
	Answered by mr W last updated on 10/Jan/23

	Commented by mr W last updated on 10/Jan/23

	$\frac{C E}{C D} = \frac{B C}{A C} \Rightarrow C E = \frac{1 \times 1}{\sqrt{5}} = \frac{\sqrt{5}}{5} = \frac{A C}{5}$ $\frac{C E}{A C} = \frac{1}{5}$ $\frac{A_{y e l l o w}}{Δ_{A C F}} = {(\frac{1}{5})}^{2} = \frac{1}{25}$ $Δ_{A C F} = \frac{A_{r e c t a n g l e}}{4}$ $\Rightarrow \frac{A_{y e l l o w}}{A_{r e c t a n g l e}} = \frac{1}{25} \times \frac{1}{4} = \frac{1}{100}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum