Question

The hypotenuse of a right angled isosceles triangle is 5 cm then its area is

• A. $\frac{21}{4}c{m}^2$
• B. $\frac{26}{4}c{m}^2$
• C. $\frac{25}{4}c{m}^2$
• D. none of these

Answer 1

The correct option is C $\frac{25}{4}c{m}^2$

In Right angled isosceles triangle two sides are equal and one angle is 90 and other two angles are 45

Then as per Pythagoras formula

$(hypotheses{)}^2=2(side{)}^2$

$\therefore (5{)}^2=2(side{)}^2$

$\Rightarrow (side{)}^2=\frac{25}{2}$\Rightarrow Side=\frac{5}{\sqrt{2}}$ cm

Then area of Right angled isosceles triangle =$\frac{1}{2}(\frac{5}{\sqrt{2}}{)}^2=\frac{25}{4}c{m}^2$