Question

Which of the following triplets are Pythagorean and why?

a)(8,15,17) b)(12,35,38) c) (14,48,51)​

Answer 1

Step-by-step explanation:

$(i) (8, 15, 17)$

$L.H.S = 82 + 152 = 289$

R.H.S = 172 = 289

L.H.S = R.H.S

∴ The given triplet is a Pythagorean.

$(ii) (18, 80, 82)$

L.H.S = 182 + 802 = 6724

R.H.S = 822 = 6724

L.H.S = R.H.S

∴ The given triplet is a Pythagorean

$(iii) (14, 48, 51)$

L.H.S = 142 + 482 = 2500

R.H.S = 512 = 2601 L.H.S ≠ R.H.S

∴ The given triplet is not a Pythagorean.

$(iv) (10, 24, 26)$

L.H.S = 102 + 242

= 676

R.H.S = 262 = 676

L.H.S = R.H.S

∴ The given triplet is a Pythagorean

Answer 2

Step-by-step explanation:

A)

-> here , in pythagorean triplet :-

$8 ^{2} + 15 ^{2} = 17 ^{2}$

.•.

$64 + 225 = 289$

therefore , A is a pythagorean triplet .

b) .

$12 { }^{2} + 35 {}^{2} = 38 {}^{2}$

:-:

$144 + 1225 = 1369$

therefore , B is not a pythagorean triplet.

C)

14² +48²=51²

:-:

196+2304= 2500

therefore, C) is not a pythagorean triplet.

hope its helpful