AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?

Correct result:

o =  72 cm
S =  216 cm²

Solution:

$$\begin{gathered} b=24\text{ cm } \\ a=b-d \\ c=b+d \\ {c}^2=a^2+b^2 \\ (b+d{)}^2=(b-d{)}^2+b^2 \\ (24+d{)}^2=(24-d{)}^2+24^2 \\ 96d=576 \\ d=576\mathrm{/}96=6 \\ a=b-d=24-6=18\text{ cm } \\ c=b+d=24+6=30\text{ cm } \\ o=a+b+c=18+24+30=72\text{ cm} \end{gathered}$$

$S={\displaystyle \frac{a\cdot b}{2}}={\displaystyle \frac{18\cdot 24}{2}}=216{\text{cm}}^2$

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