Two squares

Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.

Result

S1+S2 =  197.1 cm2

Solution:

a1a2=52=o1o2 73=o1+o2=4(a1+a2)  a1=5734(5+2)=13.0357 cm a2=2734(5+2)=5.2143 cm S1=a12=169.93 cm2 S2=a22=27.19 cm2 S=S1+S2197.1 cm2\dfrac{a_1}{a_2} = \dfrac{ 5}{ 2} = \dfrac{ o_1 }{ o_2 } \ \\ 73 = o_1 + o_2 = 4( a_1 + a_2 ) \ \\ \ \\ a_1 = \dfrac{ 5 \cdot 73 }{ 4 \cdot (5+2)} = 13.0357 \ cm \ \\ a_2 = \dfrac{ 2 \cdot 73 }{ 4 \cdot (5+2)} = 5.2143 \ cm \ \\ S_1 = a_1^2 = 169.93 \ cm^2 \ \\ S_2 = a_2^2 = 27.19 \ cm^2 \ \\ S = S_1 + S_2 \doteq 197.1 \ \text{cm}^2



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