Question

7. If the area of an isosceles right triangle is 8 cm², then the perimeter of the triangle is

Answer 1

Answer:

8 + 4√2 cm

Step-by-step explanation:

Let's say the length of the equal sides is a and the length of the hypotenuse is b.

Then its area is $\frac{1}{2}a^{2}$, and its perimeter is a + a + b = 2a + b.

$\frac{1}{2}a^{2} = 8 cm^{2}$

⇒ a² = 16 cm²

⇒ a = 4 cm

Using Pythagoras' Theorem, b² = a² + a² = 2a²

⇒ b = (√2)a = 4√2 cm

Hence perimeter is 8 + 4√2 cm