An isosceles right-angled triangle has hypotenuse length as 10 units. What is the area of the triangle (in square units)?

Correct option is B

Given:

Right angled isosceles triangle has hypotenuse of 10 cm

Formula Used:

Pythagoras’ Theorem
​$$H^2 = P^2 +B^2$$​

Area of triangle $$= \frac{1}{2} \times b \times h$$​ 

Solution:

Here hypotenuse is the non equal side of the isosceles triangle as sides containing right angles are base and perpendicular

Let the equal sides(base and perpendicular) be x

Then $$x^2 +x^2 = 10^2$$​​

​$$2x^2 = 100$$​​

​$$x^2 = 50$$​​

​$$x= \sqrt{50} = 5\sqrt{2}$$​​

Area of triangle = $$\frac{1}{2} \times 5 \sqrt{2}\times 5\sqrt{2} = \frac{1}{2} \times 25 \times 2 = 25cm^2$$​​