Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm².

Correct answer:

x =  24

Step-by-step explanation:

$$\begin{gathered} S=ab\mathrm{/}2=24 \\ 2\cdot 24=0.75a^2 \\ a=\sqrt{2\cdot 24\mathrm{/}0.75}=8cm \\ b=0.75a=6cm \\ {c}^2=a^2+b^2 \\ c=\sqrt{a^2+b^2}=10cm \\ x=a+b+c=8+6+10=24 \end{gathered}$$

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