Question

find the length of the unknown sides in following right angled triangle using Pythagoras property x, 15cm, 12cm​

Answer 1

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9 cm.

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Pythagoras theorem is :-

$\small \color{cream}{ { ( \red { base}) }^{2} + {( \red{height})}^{2} = {( \red{hypotenuse})}^{2} }$

But, here we have to find the height :-

$\tt \small = >{(height)}^{2} = {(hypotenuse)}^{2} - {(base)}^{2}$

Applying all the values :-

$= > {(x)}^{2} = {(15)}^{2} - {(12)}^{2}$

$= > {x}^{2} = 225 - 144$

$= > {x}^{2} = 81$

$= > x = \sqrt{81} = 9 \: cm$

So, length of the unknown side in this right angled triangle 9 cm.

Answer 2

Given :

• Base = 12 cm
• Hypotenuse = 15 cm

To Find :

• Perpendicular = x = ?

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SolutioN :

✬ Formula Used :

• Hypotenuse² = Base² + Perpendicular²

✬ Calculating the Value of x :

$➺ \qquad \;$ Hypotenuse² = Base² + Perpendicular²

$\\ ➺ \qquad \;$ 15² = 12² + x²

$\\ ➺ \qquad \;$ 225 = 144 + x²

$\\ ➺ \qquad \;$ 225 - 144 = x²

$\\ ➺ \qquad \;$ 81 = x²

$\\ ➺ \qquad \;$ √81 = x

$\\ ➺ \qquad \; {\pmb{\purple{\underline{\underline{\frak{ x = 9 \; cm }}}}}}$

✬ Therefore :

Value of x is 9 cm .

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