Rectangle

The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.

Result

u =  91 cm
S =  2940 cm2

Solution:

o=238 cm s=a+b=o/2 s=o/2=238/2=119 cm  a=s⋅ 55+12=119⋅ 55+12=35 cm b=s⋅ 125+12=119⋅ 125+12=84 cm  u=a2+b2=352+842=91 cmo=238 \ \text{cm} \ \\ s=a+b=o/2 \ \\ s=o/2=238/2=119 \ \text{cm} \ \\ \ \\ a=s \cdot \ \dfrac{ 5 }{ 5+12 }=119 \cdot \ \dfrac{ 5 }{ 5+12 }=35 \ \text{cm} \ \\ b=s \cdot \ \dfrac{ 12 }{ 5+12 }=119 \cdot \ \dfrac{ 12 }{ 5+12 }=84 \ \text{cm} \ \\ \ \\ u=\sqrt{ a^2+b^2 }=\sqrt{ 35^2+84^2 }=91 \ \text{cm}
S=a⋅ b=35⋅ 84=2940 cm2S=a \cdot \ b=35 \cdot \ 84=2940 \ \text{cm}^2

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