Question

An isosceles right-angled triangle has area $200c{m}^2$ What is the length of its hypotenuse $?$

• A. $20\sqrt{2}$ cm
• B. $30\sqrt{2}$ cm
• C. $70\sqrt{2}$ cm
• D. $80\sqrt{2}$ cm

Answer 1

The correct option is A $20\sqrt{2}$ cm

In an isosceles right angled triangle, the two sides on the right angle are equal
Let the equal side be $a$
Hence, hypotenuse of the isosceles right angled triangle of side $a=\sqrt{a^2+a^2}=\sqrt{2}a$
In the isosceles right triangle, the base and height $=a$
Hence, area of the triangle $=\frac{1}{2}\times base\times height=$
$\frac{1}{2}\times a\times a=200$ sq cm
$=>a^2=400$
$=>a=20cm$
And the hypotenuse $=\sqrt{2}a=20\sqrt{2}cm$