Question

Find the length of the hypotenuse of an isosceles right-angled triangle whose area is $200c{m}^2$. Also, find its perimeter. [Given: $\sqrt{2}=1.41$]

Answer 1

Let two sides of an isosceles right-angled triangle are of measure "a"
Area of triangle $=200c{m}^2$. (given)
$\Rightarrow 200=\frac{1}{2}\left(a^2\right)$
$\Rightarrow a=20cm$
Now,
Hypotenuse
$=\sqrt{(a^2+a^2)}=\sqrt{\left(2a^2\right)}=\sqrt{2}a$
$=20\sqrt{2}$
$=20\times 1.414$
$=28.28$
$\Rightarrow$ Hypotenuse is $28.28cm$

Perimeter of triangle $=$ Sum of all the sides $=2a+$ Hypotenuse
$=40+28.28$
$=68.28$
$\Rightarrow$ Perimeter of triangle is $68.28cm$.