A photograph

A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.


a =  39.846 cm
b =  29.885 cm
c =  20 cm


S1=a2 b=3/4 a c=20 S2=b c S1S2=990   a23/4 a 20=990 a215a990=0  p=1;q=15;r=990 D=q24pr=15241(990)=4185 D>0  a1,2=q±D2p=15±41852=15±34652 a1,2=7.5±32.345787979272 a1=39.845787979272 a2=24.845787979272   Factored form of the equation:  (a39.845787979272)(a+24.845787979272)=0  a=a1=39.845839.845839.846 cmS_{1}=a^2 \ \\ b=3/4 \cdot \ a \ \\ c=20 \ \\ S_{2}=b \cdot \ c \ \\ S_{1}-S_{2}=990 \ \\ \ \\ \ \\ a^2 - 3/4 \cdot \ a \cdot \ 20=990 \ \\ a^2 -15a -990=0 \ \\ \ \\ p=1; q=-15; r=-990 \ \\ D=q^2 - 4pr=15^2 - 4\cdot 1 \cdot (-990)=4185 \ \\ D>0 \ \\ \ \\ a_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 15 \pm \sqrt{ 4185 } }{ 2 }=\dfrac{ 15 \pm 3 \sqrt{ 465 } }{ 2 } \ \\ a_{1,2}=7.5 \pm 32.345787979272 \ \\ a_{1}=39.845787979272 \ \\ a_{2}=-24.845787979272 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -39.845787979272) (a +24.845787979272)=0 \ \\ \ \\ a=a_{1}=39.8458 \doteq 39.8458 \doteq 39.846 \ \text{cm}

Checkout calculation with our calculator of quadratic equations.

b=3/4 a=3/4 39.8458=29.8845=29.885 cmb=3/4 \cdot \ a=3/4 \cdot \ 39.8458=29.8845=29.885 \ \text{cm}
c=20  S1=a2=39.845821587.7037 cm2 c=S2=b c=29.8845 20=597710=597.7 cm2=20 cmc=20 \ \\ \ \\ S_{1}=a^2=39.8458^2 \doteq 1587.7037 \ \text{cm}^2 \ \\ c=S_{2}=b \cdot \ c=29.8845 \cdot \ 20=\dfrac{ 5977 }{ 10 }=597.7 \ \text{cm}^2=20 \ \text{cm}

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