Question

Which of the following triplets does not form a right triangle?
a. 4,3,5
b. 6,8,10
c. 0.7,2.4,2.5
d.12,34,35
plz. help​

Answer 1

12,34,35

as

A.T.Q Pythagoras Theorem

12^²+34^²is not equal to 35^²

144+1156 is not equal to 1225

1300 is not equal to 1225

Answer 2

Answer:

Right Angle Triangle :

Let us know some information about right angle triangle :

• A right triangle is a three-sided closed shape, that has one perpendicular side. 
• One angle is always 90° or right angle.
• The side opposite angle 90° is the hypotenuse.
• The hypotenuse is always the longest side.
• The sum of the other two interior angles is equal to 90°.
• The other two sides adjacent to the right angle are called base and perpendicular.
• In a right-angled triangle, the hypotenuse is the longest side. 
• The area of the right-angle triangle is equal to half of the product of adjacent sides of the right angle, i.e.,

$\begin{gathered}\end{gathered}$

Concept :

Let us understand the concet before going to solve the question :

➠ Let use the method of trial and error method to check whether which one of the options is not a right-angled triangle with the help of the Pythagoras theorem, 

$\bigstar \: \underline{\boxed{\sf{(Hypotenuse)^{2} =(side \: one)^{2} + (side \: two)^{2}}}}$

➠ Substitute the values in the formula and check if L.H.S is equal to R.H.S, the one which is not equal is the required answer.

$\begin{gathered}\end{gathered}$

Solution :

In a right-angled triangle, the hypotenuse is the longest side. 

(A). 4, 3, 5

Here :-

• → Hypotenuse = 5
• → Side one = 4
• → Side two = 3

Now, according to the question :-

${\dashrightarrow{\sf{(Hypotenuse)^{2} =(side \: one)^{2} +(side \: two)^{2}}}}$

${\dashrightarrow{\sf{(5)^{2} =(4)^{2} +(3)^{2}}}}$

${\dashrightarrow{\sf{(5 \times 5)=(4 \times 4) +(3 \times 3)}}}$

${\dashrightarrow{\sf{25=16 + 9}}}$

${\dashrightarrow{\sf{25 = 25}}}$

${\dashrightarrow{\sf{LHS = RHS}}}$

∴ The sides are of right-angled triangles

━┅━┅━┅━┅━┅━┅━┅━┅━┅━

(B). 6, 8, 10

Here :-

• → Hypotenuse = 10
• → side one = 6
• → side two = 8

Now, according to the question :-

${\dashrightarrow{\sf{(Hypotenuse)^{2} =(side \: one)^{2} +(side \: two)^{2}}}}$

${\dashrightarrow{\sf{(10)^{2} =(6)^{2} +(8)^{2}}}}$

${\dashrightarrow{\sf{(10 \times 10)=(6 \times 6) +(8 \times 8)}}}$

${\dashrightarrow{\sf{100 = 36 + 64}}}$

${\dashrightarrow{\sf{100 =100}}}$

${\dashrightarrow{\sf{LHS = RHS}}}$

∴ The sides are of right-angled triangles

━┅━┅━┅━┅━┅━┅━┅━┅━┅━

(C). 0.7, 2.4, 2.5

Here :-

• → Hypotenuse = 2.5
• → side one = 0.7
• → side two = 2.4

Now, according to the question :-

${\dashrightarrow{\sf{(Hypotenuse)^{2} =(side \: one)^{2} +(side \: two)^{2}}}}$

${\dashrightarrow{\sf{(2.5)^{2} =(0.7)^{2} +(2.4)^{2}}}}$

${\dashrightarrow{\sf{(2.5 \times 2.5) =(0.7 \times 0.7)+(2.4 \times 2.4)}}}$

${\dashrightarrow{\sf{6.25 =0.49+5.76}}}$

${\dashrightarrow{\sf{6.25 =6.25}}}$

${\dashrightarrow{\sf{LHS = RHS}}}$

∴ The sides are of right-angled triangles.

━┅━┅━┅━┅━┅━┅━┅━┅━┅━

(D). 12, 34, 35

Here :-

• → Hypotenuse = 35
• → side one = 12
• → side two = 34

Now according to the question :-

${\dashrightarrow{\sf{(Hypotenuse)^{2} =(side \: one)^{2} + (side \: two)^{2}}}}$

${\dashrightarrow{\sf{(35)^{2} =(12)^{2} + (34)^{2}}}}$

${\dashrightarrow{\sf{(35 \times 35) =(12 \times 12) + (34 \times 34)}}}$

${\dashrightarrow{\sf{1225 =144 + 1156}}}$

${\dashrightarrow{\sf{1225 =1300}}}$

${\dashrightarrow{\sf{LHS \neq RHS}}}$

∴ These three sides do not make a right-angled triangle.

Hence, only option (d) is the triplet which is not a right-angled triangle.