Rectangle

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

Correct answer:

u =  91 cm
S =  2940 cm²

Step-by-step explanation:

$$\begin{gathered} o=238\text{cm} \\ s=o/2=238/2=119\text{cm} \\ s=a+b \\ a:b=5:12 \\ a=s\cdot \frac{5}{5+12}=119\cdot \frac{5}{5+12}=35\text{cm} \\ b=s\cdot \frac{12}{5+12}=119\cdot \frac{12}{5+12}=84\text{cm} \\ u=\sqrt{a^2+b^2}=\sqrt{35^2+84^2}=91\text{cm} \end{gathered}$$

$S=a\cdot b=35\cdot 84=2940{\text{cm}}^2$

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