Question

What is the missing number in each of the following Pythagorean triplets.
(i).6,?,10
(ii). ?,16, 20
(iii). 9,12,?
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Answer 1

i) 8

ii) 12

iii) 15

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Answer 2

The missing number in each Pythagorean triplet is

(i) 6,9,10

(ii) 12,16,20

(iii) 9,12,15

Step-by-step explanation:

Given:

Pythagorean triplets are given as

6, ?, 10

?, 16, 20

9, 12 ,?

To find:

The missing side

Solution:

The pairs are Pythagorean triplets

According Pythagoras theorem

(hypotenuse)²= (side 1)²+ (side 2)²

For the first pair, (i)6,?,10, let the missing side be x

The longest and third side 10 will be our hypotenuse and 6 will be our side 1

∴ (10)²= (6)²+ (x)²

∴ 100= 36+ x²

∴ 100-36= x²

∴ 64= x²

∴ x²=64

∴ x=√64

∴ x= 9 units

For the second pair, (ii). ?,16, 20  let the missing side be y

20 being the third side & the longest length will be our hypotenuse, and 16 will be our side 2

∴ (20)²= y²+(16)²

∴ 400= y²+ 256

∴ 400-256= y²

∴  y²=144

∴  y = √144

∴  y = √144

∴  y =12 units

For the third pair, (iii) 9,12,? let the missing side hypotenuse be z

The length 9 will be our side 1 and 12 will be our side 2

∴ (z)²= (9)²+ (12)²

∴ z²= 81+ 144

∴ z²= 225

∴  z= √225

∴  z= 15 units

Thus the Pythagorean triplets will be as 6,9,10; 12,16,20; 9,12,15

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