November 26th, 2014, 04:44 AM  #1 
Newbie Joined: Nov 2014 From: Singapore Posts: 1 Thanks: 0  Find the area of the triangle
Hello, I'd like to know the how to derive the area of the triangle. I have tried the steps shown in the attachments. Where have I gone wrong? Last edited by skipjack; November 26th, 2014 at 10:51 AM. 
November 26th, 2014, 06:39 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,049 Thanks: 680 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
i) Let y = AF; and ii) Create a new point G which lies on CD vertically above F. Since A'E = x, $\displaystyle DA' = \sqrt{x^2  (10x)^2} = \sqrt{(x(10x))(x+(10x))} = \sqrt{20(x5)} = 2\sqrt{5x25}$ $\displaystyle Area(AEF) = Area(A'EF) = A$ $\displaystyle 2Area(AEF) + Area(A'ED) + Area(A'FG) = Area(AFGD)$ $\displaystyle 2A + \frac{1}{2}(10x)(2\sqrt{5x25}) + \frac{1}{2}\cdot 10(y2\sqrt{5x25}) = 10y$ $\displaystyle 2A = (x10)\sqrt{5x25} + 5y + 10\sqrt{5x25}$ $\displaystyle 2A = 5y + x\sqrt{5x25}$ $\displaystyle Area(AEF) = A = \frac{xy}{2}$ Therefore, $\displaystyle y = \frac{2A}{x}$. Consequently, $\displaystyle 2A = \frac{10A}{x} + x\sqrt{5x25}$ $\displaystyle 2A\left(1  \frac{5}{x}\right) = x\sqrt{5x25}$ $\displaystyle A = \frac{x\sqrt{5x25}}{2\left(1  \frac{5}{x}\right)}$ $\displaystyle A = \frac{x^2\sqrt{5x25}}{2(x  5)}$ Multiplying top and bottom by $\displaystyle \sqrt{5x25}$ gives $\displaystyle A = \frac{x^2 \cdot 5(x5)}{2(x  5)\sqrt{5x25}}$ $\displaystyle A = \frac{5x^2}{2\sqrt{5x25}}$ Last edited by Benit13; November 26th, 2014 at 06:42 AM. 
November 26th, 2014, 11:40 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,910 Thanks: 1382  You incorrectly identified the triangle similar to triangle EDA'. I'll use Benit13's notation and ignore the inappropriate "cm" in the diagram. By similar triangles, DA'/GF = EA'/A'F = x/y, and so DA' = 10x/y. As (10x/y)² + (10  x)² = x², y² = 100x²/(20x  100). Hence area(A'EF) = area(AEF) = xy/2 = 5x²/(2√(5x  25)) (since x > 5). Can you make any progress with part (b) of the question? 

Tags 
area, find, triangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
find area of triangle (linear algebra )  Juan Victor  Algebra  6  November 6th, 2014 06:10 AM 
Area of triangle AEF  Albert.Teng  Algebra  5  February 19th, 2013 10:52 PM 
Find the area of ??triangle  zgonda  Algebra  4  September 26th, 2011 10:27 AM 
Area of a Triangle  julian21  Algebra  1  October 15th, 2010 08:34 PM 
area of eq. triangle vs. area of square  captainglyde  Algebra  1  February 19th, 2008 08:55 AM 