Question

I need to find right angle triangle sides (a=?, b=?, c=?), cathetus-cathetus=1 (a-b=1) and perimeter is 12.

Answer 1

Sides of triangle = 3 , 4 and 5

Step-by-step explanation:

We have a - b = 1 --------------Equation 1

Perimeter = 12

a + b + c = 12 --------------Equation 2

And we have by Pythagoras theorem, c² = a² + b² --------------Equation 3

From equation 2 we have c = 12 -a -b, substituting in equation 3

`(12 -a -b)^2=a^2+b^2\\ \\ 144+a^2+b^2-24a-24b+2ab=a^2+b^2\\ \\ ab-12a-12b=-72` --------------Equation 4

From equation 1 we have a = 1+b, substituting in equation 4

`(1+b)b-12(1+b)-12b=-72\\ \\ b+b^2-12-12b-12b=-72\\ \\ b^2-23b+60=0\\ \\ (b-3)(b-20)=0`

b = 20 is not possible since perimeter is only 12.

So, b = 3

Substituting in equation 1 and 2

a - 3 = 1, a = 4

3 + 4 + c = 12, c= 5

Sides of triangle = 3 , 4 and 5