Rectangle 35

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

Correct answer:

S =  360 cm²

Step-by-step explanation:

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

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