Question

An isosceles right triangle has area 8cm^2. Find the length of its hypotenuse
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Answer 1

Answer:

Length of its hypotenuse = $\sf{4\sqrt{2}}$

Step-by-step explanation:

Given :

Area of the right isosceles triangle = 8 cm²

To find :

The length of the hypotenuse

Conecpt :

To find the length of its hypotenuse first find the base . So , to find the base or perpendicular use this formula -:

Let the AB and BC be x

$\boxed{\sf{8=\dfrac{1}{2}\times x\times x}}$

After that to find the length of its hypotenuse use the Pythagoras theorem .

$\boxed{\sf{{AC}^{2}={AB}^{2}+{BC}^{2}}}$

Solution :

Base -:

$:\implies\sf{8=\dfrac{1}{2}\times x\times x}$

$:\implies\sf{8\times2={x}^{2}}$

$:\implies\sf{16={x}^{2}}$

$:\implies\sf{\sqrt{16}=x}$

$:\implies\sf{4cm=x}$

Length of its hypotenuse -:

$:\implies\sf{{AC}^{2}={4}^{2}+{4}^{2}}$

$:\implies\sf{AC=\sqrt{(4\times4)+(4\times4)}}$

$:\implies\sf{AC=\sqrt{16+16}}$

$:\implies\sf{AC=\sqrt{32}}$

$:\implies\sf{AC=4\sqrt{2}}$

So , the length of its hypotenuse is $\sf{4\sqrt{2}}$ .