Question

does anyone know this?​

Answer 1

Answer:

4. (d) (6,8,10)

5. (b) 50

6. (c) 2

Answer 2

Hi buddy :)

4. Pythagoras Triplet :

$\large \tt \: we \: \: know \: \: theoram$

$\large \leadsto \: \rm \: {h}^{2} = {b}^{2} + {p}^{2}$

• h = Hypotenuse

• b = base

• p = perpendicular

$\\ \large \: so..$

In given options :

a) 4,5,6

$\: \: \: \: \: \: \: \: \: \: \large \sf \: hypotenuse \: \: is \: \: longest \: \: side$

So, h = 6

By Pythagoras Theorem :

$\\ \large \rm \implies \: {6}^{2} = {4}^{2} + {5}^{2} \\ \\ \large \rm \implies \: 36 = 16 + 25 \\ \\ \large \sf \mapsto \: 36 \not = 41$

Solving with this method for all..

• We come at option d)

( 6, 8 , 10)

By Pythagoras Theorem

$\\ \large \rm \implies \: {10}^{2} = {6}^{2} + {8}^{2} \\ \\ \large \implies \rm \: 100 = 36 + 64 \\ \\ \large \therefore \: 100 = 100$

$\\ \large \underline{ \boxed{ \sf \: answer =d.. \: (10 \: . \: 6 \: .\: 8)}}$

5. Natural numbers between 25² , 26²

As,

$\\ \large \sf \: these \: \: number \: \: are \: \: consecutive \:$

So ,

Their Sum = difference im thier square

$\\ \large \rm \implies \: 25 + 26$

c) 51 (answer)

• Did we do it correctly? ◇ Check ◇

$\\ \large \tt \mapsto \: {25 }^{2} - {26}^{2} \\ \\ \large \tt \implies \: 625 - 676 \\ \\ \large \sf \: = 51$

51 = 51

• L.H.S = R.H.S

Hence Proved

6. 162 × ? = perfect square

Prime Factorisation

$\\ \large \rm \: = 2 \times 3 \times 3 \times 3 \times 3$

• Pairing

$\\ \large \sf \: = 2 \times \bar 3 \times \bar3 \times \bar3 \times \bar3$

2 is left alone

$\\ \large \rm \therefore \: \: smallest \: \: number = 2$

162 × 2 = 324

$\\ \large \mapsto \rm \: 324 = {18}^{2}$

So, a perfect square

answer = option c) 2