My Math Forum area of a square

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September 21st, 2012, 11:16 PM   #1
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area of a square

[attachment=0:36c0in22]area of a square.jpg[/attachment:36c0in22]

$\text Ans :\,\, 392 \,cm^2\text$
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 September 22nd, 2012, 02:11 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: area of a square From figure 1, we see that the area of triangle ABC is 882 cm². From figure 2, after applying Pythagoras, we may find the area A of the square from: $\frac{9}{4}A=882\text{ cm^2}$ $A=392\text{ cm^2}$
 September 22nd, 2012, 02:50 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: area of a square In figure 2 the side of the square trisects the hypotenuse, which is of length $^{^{6\sqrt{98}}}$, so $^{^{A\,=\,$$2\sqrt{98}$$^2\,=\,392.}}$
 September 22nd, 2012, 09:16 AM #4 Math Team   Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408 Re: area of a square Hello, Albert.Teng! From figure 1, we see that the side of the square is 21 cm. And $AB\,=\,BC\,=\,42\text{ cm.}$ Code:  A * | * R | o 42 | /:::\ Q So:::::::o |x\:::/x * B *---o-------* C P : - 42 - - : $\text{We have square }PQRS\text{ with sides: }\,PQ\,=\,QR\,=\,RS\,=\,SP\,=\,x.$ $\text{In isosceles right triangle }PQC\text{, we have: }\,PC \,=\,x\sqrt{2}$ $\text{In isosceles right triangle }SBP\text{, we have: }\,BP \,=\,\frac{x}{\sqrt{2}}$ $\text{Hence: }\:x\sqrt{2}\,+\,\frac{x}{\sqrt{2}} \:=\:42 \;\;\;\Rightarrow\;\;\;x\left(\sqrt{2}\,+\,\frac{1 }{\sqrt{2}}\right) \:=\:42$ [color=beige]. . . . . . . . [/color]$x\left(\frac{3}{\sqrt{2}}\right) \:=\:42 \;\;\;\Rightarrow\;\;\;x \:=\:42\left(\frac{\sqrt{2}}{3}\right) \:=\:14\sqrt{2}$ $\text{Therefore, the area of the square is: }\:x^2 \:=\:\left(14\sqrt{2}\right)^2 \:=\:392$
 September 22nd, 2012, 09:23 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 The area of the square in Figure 1 is AC²/8, and the area of the square in Figure 2 is AC²/9. (8/9)441 cm² = 392 cm².

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