Rectangle 3-4-5

The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.

Correct answer:

S =  192 cm²

Step-by-step explanation:

$$\begin{gathered} u=20 \\ {3}^2+4^2=5^2 \\ (3x{)}^2+(4x{)}^2=(5x{)}^2 \\ a=3\mathrm{/}5\cdot u=3\mathrm{/}5\cdot 20=12\text{ cm } \\ b=4\mathrm{/}5\cdot u=4\mathrm{/}5\cdot 20=16\text{ cm } \\ S=a\cdot b=12\cdot 16=192{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ d=\sqrt{a^2+b^2}=\sqrt{12^2+16^2}=20\text{ cm } \\ d=u \end{gathered}$$

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