RT perimeter

The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.

Result

o =  30 cm

Solution:

a=b7 a=c8 a2+b2=c2 a2+(a+7)2=(a+8)2 a22a15=0 a=5 b=a+7=5+7=12 c=a+8=5+8=13 o=a+b+c=5+12+13=30 cma=b-7 \ \\ a=c-8 \ \\ a^2+b^2=c^2 \ \\ a^2+(a+7)^2=(a+8)^2 \ \\ a^2-2a-15=0 \ \\ a=5 \ \\ b=a+7=5+7=12 \ \\ c=a+8=5+8=13 \ \\ o=a+b+c=5+12+13=30 \ \text{cm}

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