Question

Which of the following are Pythagorean triplets!
Justify
3,5,4​

Answer 1

Answer:

Longest side ( Hypotenuse)= 5

ATQ

H^2= P^2+B^2

(5)^2=(3)^2+(4)^2

25=9+16

25=25

Hence it is a Pythagorean triplet.

Answer 2

Answer:

$\huge{\pink{\boxed{\green{\underline{\sf{THIS\:IS\:A\:PHYTHAGORAS\:TRIPLET}}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

☆ According to phythagoras triplet:

☆ Largest side of triangle is the hypotenuse of right angled triangle

☆ The angle opposite to that side is 90°

☆ The square of hypotenuse is equal to the of square of their sum of their height and base.

${\pink{ \boxed{ \green{ \therefore \: hypotenuse = 5cm}}}} \\ {\pink{ \boxed{ \green{ \therefore \: base = 3cm}}}} \\ {\pink{ \boxed{ \green{ \therefore \: perpendicular = 4cm}}}}$

☆ Use h^{2} = p^{2} + b^{2}

$\to{h}^{2} = {p}^{2} + {b}^{2} \\ \\ \: \: \: \: \: { \red {\boxed{ lhs }}} \\ \to {h}^{2} \\ \to \: {5}^{2} \\ \to \: 25 \\ \\ \: \: \: \: \: \: {\red { \boxed{rhs}}} \\ \to {p}^{2} + {b}^{2} \\ \to {4}^{2} + {3}^{2} \\ \to16 + 9 \\ \to25 \\ { \purple{ \boxed {\red{lhs = rhs}}}}$

$\huge{\pink{\boxed{\green{\underline{\sf{THIS\:IS\:A\:PHYTHAGORAS\:TRIPLET}}}}}}$

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