a)

$5^2+7^2=x^2$  

$25+49=x^2$  

$74=x^2$  

$x=\sqrt{74}\left[\text{cm}\right]$  

 

$x^2+8^2=d^2$  

$74+64=d^2$  

$138=d^2$  

$d=\sqrt{138}\left[\text{cm}\right]$  

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b)

 

$V=a^2\cdot c$  

$36=a^2\cdot c\mid :a^2$  

$\frac{36}{a^2}=c$  

 

$P_b=4\cdot a\cdot c$  

$48=4\cdot a\cdot c\mid :4$  

$12=a\cdot c$  

$12=a\cdot \frac{36}{a^2}$  

$12=\frac{36}{a}\mid \cdot a$  

$12a=36\mid :12$  

$a=3$  

 

$c=\frac{36}{a^2}$  

$c=\frac{36}{3^2}$  

$c=\frac{36}{9}$  

$c=4$  

 

Przekątna podstawy wynosi  $a\sqrt{2}\Rightarrow a\sqrt{2}=3\sqrt{2}$  

 

${\left(3\sqrt{2}\right)}^2+4^2=d^2$  

$9\cdot 2+16=d^2$  

$18+16=d^2$  

$34=d^2$  

$d=\sqrt{34}$