Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.

Correct result:

S =  60 cm²

Solution:

$$\begin{gathered} a=12\text{ cm } \\ u=8+b \\ {u}^2=a^2+b^2=12^2+b^2 \\ (8+b{)}^2=12^2+b^2 \\ 16b=80 \\ b=80\mathrm{/}16=5\text{ cm } \\ u=\sqrt{a^2+b^2}=\sqrt{12^2+5^2}=13\text{ cm } \\ u=8+b \\ S=a\cdot b=12\cdot 5=60{\text{cm}}^2 \end{gathered}$$

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