Question

determine 13 cm 12 cm 5 cm forms a right angled triangle if yes find the hypotenuse​

Answer 1

We know according to pythagorous theorem that the square of the longest side is equal to the sum of squares of other two sides.

so,

the longest side given over here in the question is: 13cm

and the other two sides are: 12cm and 5cm.

now,

H² = B² + P²

13² = 12² + 5²

169 = 144 + 25

169 = 169

So, 

yes the triangle given over here is right angled triangle as the square of the longest side is equal to the sum of squares of the other two sides.

now, 

by construction draw an altitude on the longest side.

now let a= 5, b=12 and c= 13 

and using heron's formula we get,

s= (a + b + c) / 2 { semi perimeter }

s= 5 + 12 + 13 / 2

s= 30 / 2

s= 15

now,

Area of the triangle = √[s(s-a)(s-b)(s-c)]

                                 = √[ 15 ( 15-5 ) ( 15-12 ) ( 15-13 )

                                 = √[ 15 ( 10 ) ( 3 ) ( 2 )

                                 = √[ 15 ( 60 )

                                 = √[  900 ]

                                 = √[ 30 × 30]

                                 = 30 cm²

now we also know that area of triangle =  × base × altitude

                                                                 =  ×  13 ×  altitude

                                                    30 × 2  = 13 ×  altitude

                                                    60 / 13 = altitude

                                                    4.6 cm = altitude

we will be taking the hypotenuse the base as the altitude is drawn from it.

Answer 2

Answer:

Yes it is.

Step-by-step explanation:

So according to the pythagoras theorem,

$a^{2}$ + $b^{2}$ = $c^{2}$

Since the biggest side is 'c',

$5^{2}$ + $12^{2}$ = $13^{2}$

25 + 144 = 169

therefore it is a right angled triangle & 13 is the hypotenuse.