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Question Number 187790 by cherokeesay last updated on 21/Feb/23

Answered by mr W last updated on 21/Feb/23

Commented by mr W last updated on 22/Feb/23

(2a−2)^2 +[((√5)−1)a]^2 =(2a)^2 +2^2 ⇒a=(4/(3−(√5)))=3+(√5) area of square =(2a)^2 =4(3+(√5))^2 =56+24(√5)≈109.666

(2a−2)2+[(5−1)a]2=(2a)2+22⇒a=43−5=3+5areaofsquare=(2a)2=4(3+5)2=56+245≈109.666

Commented by cherokeesay last updated on 22/Feb/23

so nice thank you sir.

sonicethankyousir.

Answered by HeferH last updated on 22/Feb/23

let 2x be the side of the square: (2x−2)^2 +(x(√5)−x)^2 =2^2 +(2x)^2 4x^2 +4−8x + 5x^2 +x^2 −2x^2 (√5) = 4 + 4x^2 6x^2 −8x−2x^2 (√5) = 0 6x −8 −2x(√5) = 0 3x−x(√5) = 4 x(3−(√5)) = 4 x = (4/(3−(√5))) ; 4x^2 =4[ ((4(3+(√5)))/(9−5))]^2 = 4(14+6(√5)) u^2 = 56+24(√5)u^2

let2xbethesideofthesquare:(2x−2)2+(x5−x)2=22+(2x)24x2+4−8x+5x2+x2−2x25=4+4x26x2−8x−2x25=06x−8−2x5=03x−x5=4x(3−5)=4x=43−5;4x2=4[4(3+5)9−5]2=4(14+65)u2=56+245u2

Commented by cherokeesay last updated on 22/Feb/23

perfect ! thank you sir.

perfect!thankyousir.

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