A right 3

A right triangle has a perimeter of 300 cm . its hypotenuse is 130cm. What are the lengths of the other sides .

Final Answer:

a =  120 cm
b =  50 cm

Step-by-step explanation:

o=300 cm c=130 cm  o = a+b+c  a+b = o−c=300 − 130 = 170  cm  c2 = a2+b2  c2=a2+(170−a)2  1302=a2+(170−a)2 −2a2+340a−12000=0 2a2−340a+12000=0 2 ...  prime number 340=22⋅5⋅17 12000=25⋅3⋅53 GCD(2,340,12000)=2  a2−170a+6000=0  p=1;q=−170;r=6000 D=q2−4pr=1702−4⋅1⋅6000=4900 D>0  a1,2​=2p−q±D​​=2170±4900​​ a1,2​=2170±70​ a1,2​=85±35 a1​=120 a2​=50  a=a1​=120=120 cm

Our quadratic equation calculator calculates it.

b=a2​  b=170−a=170−120=50   Verifying Solution:  c2​=a2+b2​=1202+502​=130 cm o2​=a+b+c=120+50+130=300 cm

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