Question

height and base of a right angle triangle are 24cm and 18 cm respectively find the length of its hypotenuse​

Answer 1

Answer:

height and base of a right angle triangle are 24cm and 18 cm respectively find the length of its hypotenuse

Step-by-step explanation:

Please do follow me.

Answer 2

• The length of the hypotenuse of a right angled triangle = 30 cm.

Diagram :

$\setlength{\unitlength}{17mm}\begin{picture}(5,5)\put(0,1){\line(0,1){1.5}}\put(0,1){\line(1,0){1.8}}\put(0,2.5){\line(6,-5){1.8}}\put(1.1,1.8){\bf{H = x}}\put(0.2,0.6){\bf{B = 18 cm}}\put(-1.3,1.6){\bf{P = 24 cm}}\put(0,1){\framebox(0.23,0.23)}\end{picture}$

Given :

• The height of a right angled triangle = 24 cm.
• The base of a right angled triangle = 18 cm.

To Find :

• The length of the hypotenuse of a right angled triangle.

Solution :

Let,

The length of the hypotense of a right angled triangle be x.

By Pythagoras theorem,

$\huge{\star} \: \: \large{\underline{\underline{ \boxed{ \bf{ {H}^{2} = {B}^{2} + {P}^{2} }}}} \: \: \: \huge \star}$

Where,

• H = hypotenuse.
• B = base.
• P = perpendicular (height).

Given,

• B = 18 cm.
• P = 24 cm.

Now, substitute the given values in the Pythagoras theorem,

$:\implies \bf {H}^{2} = {(18 \: cm)}^{2} + {(24 \: cm)}^{2} \\ \\ \\ :\implies \bf {H}^{2} = 324 \: {cm}^{2} + 576 \: {cm}^{2} \\ \\ \\ :\implies \bf {H}^{2} = 900 \: {cm}^{2} \\ \\ \\ :\implies \bf H = \sqrt{900 \: {cm}^{2} } \\ \\ \\ :\implies \bf H = 30 \: cm \\ \\ \\ \: \: \: \bf \therefore \: \: H = 30 \: cm$

Hence,

The length of the hypotenuse of a right angled triangle is 30 cm.