Question

Question 1
An isosceles right triangle has area $8c{m}^2$. The length of its hypotenuse is

Answer 1

Given, area of an isosceles right triangle = $8c{m}^2$
Area of an isosceles triangle $=\frac{1}{2}(Base\times Height)$
$\Rightarrow 8=\frac{1}{2}(Base\times Base)$
[$\because$ base = height, as triangle is an isosceles triangle]
$\Rightarrow (Base{)}^2=16\Rightarrow Base=4cm$
In $\Delta ABC$, using Pythagoras theorem,
$A{C}^2=A{B}^2+B{C}^2=4^2+4^2=16+16$
$\Rightarrow A{C}^2=32\Rightarrow AC=\sqrt{32}cm$
[taking positive square root because length is always positive]
Hence, the length of its hypotenuse is $\sqrt{32}cm$