# 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?

Result

o =  72 cm
S =  216 cm2

#### Solution:

$b=24 \ \text{cm} \ \\ a=b-d \ \\ c=b+d \ \\ c^2=a^2+b^2 \ \\ (b+d)^2=(b-d)^2+b^2 \ \\ \ \\ (24+d)^2=(24-d)^2+24^2 \ \\ 96d=576 \ \\ d=576/96=6 \ \\ \ \\ a=b-d=24-6=18 \ \text{cm} \ \\ c=b+d=24+6=30 \ \text{cm} \ \\ \ \\ o=a+b+c=18+24+30=72 \ \text{cm}$
$S=\dfrac{ a \cdot \ b }{ 2 }=\dfrac{ 18 \cdot \ 24 }{ 2 }=216 \ \text{cm}^2$

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