Let:
Length of each of the equal sides of the isosceles right-angled triangle = a = 10 cm
And.
Base = Height = a
Area of isosceles right – angled triangle = \(\frac{1}{2}\times Base \times Height\)
The hypotenuse of an isosceles right – angled triangle can be obtained using Pythagoras’ theorem
If h denotes the hypotenuse, we have:
h2 = a2 + a2
\(\Rightarrow\) h = 2a2
\(\Rightarrow\) h = \(\sqrt{2a}\)
\(\Rightarrow\) h = \(10\sqrt{2}\) cm
\(\therefore\) Perimeter of the isosceles right-angled triangle = 2a + \(\sqrt{2}a\)
= 2 x 10 + 1.41 x 10
= 20 + 14.1
= 34.1 cm
