# Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.

Correct result:

S =  360 cm2

#### Solution:

$u=30 \ \text{cm} \ \\ a=2b \ \\ u^2=a^2 + b^2 \ \\ S=ab=360 \ \text{cm}^2 \ \\ u^2=(2b)^2 + b^2 \ \\ u^2=5 \ b^2 \ \\ b=u/\sqrt{ 5 }=30/\sqrt{ 5 } \doteq 6 \ \sqrt{ 5 } \doteq 13.4164 \ \\ a=2 \cdot \ b=2 \cdot \ 13.4164 \doteq 12 \ \sqrt{ 5 } \doteq 26.8328 \ \\ S=a \cdot \ b=26.8328 \cdot \ 13.4164=360 \ \text{cm}^2 \ \\ v=\sqrt{ a^2+b^2 }=\sqrt{ 26.8328^2+13.4164^2 }=30 \ \text{cm}$

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