Question

Answer number 1 please.​

Answer 1

$\bold{\huge{\pink{\underline{ Solution }}}}$

$\bold{\underline{ Given :-}}$

• We have a right angled triangle whose two sides that is perpendicular and hypotenuse are 5 units and 12 units

$\bold{\underline{ Let's\: Begin:-}}$

According to the Pythagoras theorem,

• Pythagoras theorem states that the sum of squares of two small sides that is perpendicular height and base are equal to the square of longest side that is hypotenuse

That is,

$\sf{\red{ ( Base)² + ( Perpendicular )² = ( Hypotenuse)²}}$

$\sf{ ( a )² + ( b )² = ( c )²}$

Subsitute the required values,

$\sf{ ( a )² + ( 5 )² = ( 13)²}$

$\sf{ a² + 25 = 169}$

$\sf{ a² = 169 - 25 }$

$\sf{ a² = 144}$

$\sf{ a = √144}$

$\sf{ a = 12}$

$\sf{\blue{ Hence,\: Length \:of \:a\: is \:12 units }}$

Answer 2

$\sf {a}^{2} = {13}^{2} - {5}^{2}$

Formula :

Base²= Hypotenuse² - Perpendicular ²

$\hookrightarrow\sf {a}^{2} = {13}^{2} - {5}^{2}$

$\hookrightarrow\sf {a}^{2} =169 - 25$

$\hookrightarrow\sf {a}^{2} =144$

$\hookrightarrow\sf {a} = \sqrt{144}$

$\hookrightarrow\sf {a} = \sqrt{12 \times 12}$

$\hookrightarrow\sf {a} = 12$

Remember the a² in formula has nothing to do with the a we have to find. :)