Question

If the hypotenuse of an isosceles right triangle is 7√2 cm ,find the area of the circle inscribed in it

Answer 1

Area is 13.25cm²
Hope it helps

Answer 2

Answer:

The area of incircle is 13.2 cm².

Step-by-step explanation:

The hypotenuse of an isosceles right triangle is 7√2 cm. Let the length of leg be x.

Using Pythagoras theorem,

$x^2+x^2=(7\sqrt{2})^2$

$2x^2=98$

$x^2=49$

$x=7$

The length of leg is 7.

Radius of a circle inscribed in a right angled triangle is

$r=\frac{leg_1+leg_2-hypotenuse}{2}$

$r=\frac{7+7-7\sqrt{2}}{2}$

$r=2.05$

The radius of circle is 2.05 cm.

The area of a circle is

$A=\pi r^2$

$A=\pi (2.05)^2$

$A=13.2$

Therefore the area of incircle is 13.2 cm².