We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
282
1
avatar+72 

 For a triangle XYZ, we use [XYZ] to denote its area.

Let ABCD be a square with side length 1. Points E and F lie on line BC and line CD, respectively, in such a way that angle EAF=45 degrees If [CEF]=1/9, what is the value of [AEF]?

 Oct 13, 2018
 #1
avatar+8337 
+2

 For a triangle XYZ, we use [XYZ] to denote its area.
Let ABCD be a square with side length 1. Points E and F lie on line BC and line CD, respectively, in such a way that angle EAF=45 degrees If [CEF]=1/9, what is the value of [AEF]?

 

Hello NerdyKid!

 

 

[ABCD] = \(1m^2\)

[CEF] = \(\frac{1}{9}m^2\)

\([CEF]=\frac{\overline{FC}^2}{2}=\frac{1}{9}m^2\\ \overline{FC}=\sqrt{\frac{2}{9}}m=\frac{\sqrt{2}}{3}m\\ \overline{DF}=1m-\overline{FC}=(1-\frac{\sqrt{2}}{3})m\)

\(2[ADF]=(1-\sqrt{\frac{2}{9}})m\cdot 1m=(1-\frac{\sqrt{2}}{3})m^2\)

\([AEF]=1m^2-[CEF]-2[ADF]\\ [AEF]=1m^2-\frac{1}{9}m^2-(1-\frac{ \sqrt{2}}{3})m^2 \\ [AEF]=1m^2-\frac{1}{9}m^2-1m^2+\frac{3\cdot \sqrt{2}}{9}m^2\\ [AEF]=\frac{3\cdot \sqrt{2}\ -1}{9} m^2 \\ \color{blue}[AEF]\approx0.3602934\ m^2\)

I have to recalculate that.

blush     asinus

I calculated it. It is true.

laugh  !

 Oct 13, 2018
edited by asinus  Oct 14, 2018
edited by asinus  Oct 14, 2018
edited by asinus  Oct 14, 2018

15 Online Users

avatar
avatar
avatar