Right-angled 82416

What are the sides of a right-angled triangle with a perimeter of 45 centimeters and a volume of 67.5 cm²?

Correct answer:

a =  18 cm
b =  7.5 cm
c =  19.5 cm

Step-by-step explanation:

o=45 cm S=67.5 cm2  o=a+b+c S=2ab​ c2=a2+b2  o2 = a2 + 2 a b + 2 a c + b2 + 2 b c + c2 o2 = 2 a b + 2 a c + 2 b c + 2 c2 o2 = 4S + 2 c (a + b + c) o2 = 4S + 2 c o  c=2⋅ oo2−4⋅ S​=2⋅ 45452−4⋅ 67.5​=239​=19.5 cm  2S = ab  2⋅ S=a⋅ (o−c−a)  2⋅ 67.5=a⋅ (45−19.5−a) a2−25.5a+135=0  p=1;q=−25.5;r=135 D=q2−4pr=25.52−4⋅1⋅135=110.25 D>0  a1,2​=2p−q±D​​=225.5±110.25​​ a1,2​=12.75±5.25 a1​=18 a2​=7.5  a=a1​=18=18 cm b=a2​=7.5=215​

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