Question

Q8. Which of the following lengths do not represent the lengths of the
sides of a right triangle?

A 12 cm, 16 cm, 20 cm
B 10 cm, 24 cm. 26 cm
C 16 cm, 30 cm, 34 cm
D 18 om 24 cm, 28 cm​

Answer 1

Answer:

) Given, a=7,cm,b=24cm and c=25cm

c

2

=a

2

+b

2

[ By using Pythagoras theorem ]

c

2

=7

2

+24

2

c

2

=49+576

c

2

=625

∴ c=25cm

Hence, the given triangle is right angled triangle.

(ii) given, a=9cm,b=16cm and c=18

c

2

=a

2

+b

2

[ By using Pythagoras theorem ]

c

2

=9

2

+16

2

c

2

=81+256

c

2

=337

∴ c=18.35cm

Hence, the given triangle is not right angled triangle.

(iii) given, a=1.6,cm,b=3.8cm and c=4cm

c

2

=a

2

+b

2

[ By using Pythagoras theorem ]

c

2

=(1.6)

2

+(3.8)

2

c

2

=2.56+14.44

c

2

=17

∴ c=4.12cm

Hence, the given triangle is not right angled triangle.

(iv) given, a=8,cm,b=10cm and c=6cm

b

2

=a

2

+c

2

[ By using Pythagoras theorem ]

b

2

=(8)

2

+(6)

2

b

2

=64+36

b

2

=100

∴ b=10cm

Hence, the given triangle is right angled triangle.

Answer 2

★ How to do :-

Here, in each question, three sides of a triangle has been given to us. We are asked to find out whether these sides form a right angled triangle or not. So, here we are going to solve the question with step by step explanation. The concept used here is the pythagoras theorem. It's always applied to a right angled triangle. It says that the sum of square of other two sides of a right-angled triangle will always equal to the hypotenuse side. So, let's solve!!

$\:$

➤ Solution (1) :-

${\tt \leadsto {AB}^{2} + {BC}^{2} = {AC}^{2}}$

Substitute the values.

${\tt \leadsto {12}^{2} + {16}^{2} = {20}^{2}}$

Find the square numbers of all the values given.

${\tt \leadsto 144 + 256 = 400}$

Add the numbers in LHS.

${\tt \leadsto 400 = 400}$

${\tt \leadsto LHS = RHS}$

It can form a right-angled triangle.

$\:$

➤ Solution (2) :-

${\tt \leadsto {AB}^{2} + {BC}^{2} = {AC}^{2}}$

Substitute the values.

${\tt \leadsto {10}^{2} + {24}^{2} = {26}^{2}}$

Find the square numbers of all the values given.

${\tt \leadsto 100 + 576 = 676}$

Add the numbers in LHS.

${\tt \leadsto 676 = 676}$

${\tt \leadsto LHS = RHS}$

It can form a right-angled triangle.

$\:$

➤ Solution (3) :-

${\tt \leadsto {AB}^{2} + {BC}^{2} = {AC}^{2}}$

Substitute the values.

${\tt \leadsto {16}^{2} + {30}^{2} = {34}^{2}}$

Find the square numbers of all the values given.

${\tt \leadsto 256 + 900 = 1156}$

Add the numbers in LHS.

${\tt \leadsto 1156 = 1156}$

${\tt \leadsto LHS = RHS}$

It can form a right-angled triangle.

$\:$

➤ Solution (4) :-

${\tt \leadsto {AB}^{2} + {BC}^{2} = {AC}^{2}}$

Substitute the values.

${\tt \leadsto {18}^{2} + {24}^{2} = {28}^{2}}$

Find the square numbers of all the values given.

${\tt \leadsto 324 + 576 = 784}$

Add the numbers in LHS.

${\tt \leadsto 900 \neq 784}$

${\tt \leadsto LHS \neq RHS}$

It cannot form a right-angled triangle.

$\:$

Hence solved !!