Constructed triangle

The perimeter of the right triangle is 18 cm. The sum of the areas of the squares constructed above its three sides is 128 cm². What is the area of the triangle?

Correct answer:

S =  9 cm2

Step-by-step explanation:

o=18 cm o = a+b+c  S1=128 cm2 S1 = a2+b2+c2  = c2 + c2  c=S1/2=128/2=8 cm  oc = a+b a2+b2 = c2  a2 + (oca)2 = c2 a2+(188a)2=82  2a220a+36=0 2 ...  prime number 20=225 36=2232 GCD(2,20,36)=2  a210a+18=0  p=1;q=10;r=18 D=q24pr=1024118=28 D>0  a1,2=2pq±D=210±28=210±27 a1,2=5±2.645751 a1=7.645751311 a2=2.354248689  a=a1=7.64587.6458 cm b = a2  cm  b=oca=1887.64582.3542 cm  S=2a b=27.6458 2.3542=9 cm2

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