Isosceles triangle - this is triangle in wich two sides are equal to one another.
Perimeter of triangle - this is a sum of all sides.
Let a,b (are legs),c (is hypotenuse) be a sides of this triangle and a=b. So, perimeter of this triangle is equal to:
\(P=a+b+c=2a+c\)
This is an right angle triangle. So, we can use a Pythagorean Theorem.
\(a^2+b^2=c^2\\a^2+a^2=c^2\\2a^2=c^2\)
But c=10 cm. So:
\(2a^2=10^2\\2a^2=100\\a^2=50\\a= \sqrt{50} =5 \sqrt{2}\)
\(b=a =5 \sqrt{2}\)
Perimeter:
\(P=2\cdot 5 \sqrt{2} +10=10 \sqrt{2} +10=10( \sqrt{2} +1)\) cm