Write the correct answer in the following: An isosceles right tri… - Vidyadip

MCQ

Write the correct answer in the following:
An isosceles right triangle has area 8cm². The length of its hypotenuse is:

A
$\sqrt{32}\text{cm}$
B
$\sqrt{16}\text{cm}$
C
$\sqrt{48}\text{cm}$
D
$\sqrt{24}\text{cm}$

✓

Answer

$\sqrt{32}\text{cm}$
Solution:
ABC is an isosceles right triangle. We have,

$\text{AB}=\text{BC}=\text{a cm}$
Area of $\triangle=\frac{1}{2}\text{base}\times\text{Height}$
$\Rightarrow\ 8=\frac{1}{2}\times\text{a}\times\text{a}$ $\big[\because\ \text{AB}=\text{BC}=\text{a cm}\big]$
$\Rightarrow\ \text{a}^2=16$ $\therefore\ \text{a}=+\sqrt{16}=4\text{cm}$
Using Pythagoras theorem,
Hypotenuse $\text{AC}=\sqrt{4^2+4^2}$
$=\sqrt{16+16}=\sqrt{32}\text{cm}$

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