Question

if the length of hypotenuse of a right angled triangle is 13cm and it's base is 5cm thn find the length of its height​

Answer 1

Answer:

12cm

Step-by-step explanation:

by Pythagoras theorm

(hypotenuse)2 +(base)2 +(perpendicular)2

so,

(13)2= (5)2+(perpendicular)2

169=25+(p)2

169-25=p2

144=p2

√144=p

p=12

the height of right angled triangle is 12 cm

Answer 2

$\sf Given \begin{cases} & \sf{Hypotenuse = \bf{13\;cm}} \\ & \sf{Base = \bf{5\;cm}} \end{cases}$

Need to find: Length of Perpendicular.

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☯ Let P be the Perpendicular of triangle.

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$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf P}\put(2.8,.3){\large\bf 5 cm}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\put(4,2.7){\large\bf 13 cm}\end{picture}$

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$\sf\underline{\bigstar\;Using\; Pythagoras\; theorem\;:}$

$\star\;{\boxed{\sf{\purple{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}}$

$:\implies\sf (13)^2 = (5)^2 + (P)^2$

$:\implies\sf 169 = 25 + P^2$

$:\implies\sf P^2 = 169 - 25$

$:\implies\sf P^2 = 144$

$:\implies\sf \sqrt{P^2} = \sqrt{144}$

$:\implies{\boxed{\sf{\pink{P = 12\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Height\;or\; Perpendicular\;of\; given\;triangle\;is\; \bf{12\;cm}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

• Pythagoras Theorem: It states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

• (Hypotenuse)² = (Base)² + (Perpendicular)²