AP RT triangle

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

Correct answer:

o =  72 cm
S =  216 cm²

Step-by-step explanation:

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

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

Try another example