Question

Verify whether the following triplets are Pythagorean or not.
(i) (8, 9, 10)
(ii) (5, 7, 12)
(iii) (3,4,5)
(v) (9, 12, 15)
(iv) (5, 12, 13)​

Answer 1

Solution:

(i) Base = 8 units

Altitude = 9 units

Hypotenuse = 10 units

= 8 + 9 > 10

= 17 > 10

$\therefore$ the following measures is a triangle.

(ii) Base = 5 units

Altitude = 7 units

Hypotenuse = 12 units

= 5 + 7 ≯ 12

= 12 ≯ 12

$\therefore$ the following measures is not a triangle.

(iii) Base = 3 units

Altitude = 4 units

Hypotenuse = 5 units

= 3 + 4 > 5

= 7 > 5

$\therefore$ the following measures is a triangle.

(iv) Base = 9 units

Altitude = 12 units

Hypotenuse = 15 units

= 9 + 12 > 15

= 21 > 15

$\therefore$ the following measures is a triangle.

(v) Base = 5 units

Altitude = 12 units

Hypotenuse = 13 units

= 5 + 12 > 13

= 17 > 15

$\therefore$ the following measures is a triangle.

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Answer 2

Answer:

(i) Base = 8 units

Altitude = 9 units

Hypotenuse = 10 units

= 8 + 9 > 10

= 17 > 10

the following measures is a triangle.

(ii) Base = 5 units

Altitude = 7 units

Hypotenuse = 12 units

= 5 + 7 ≯ 12

= 12 ≯ 12

the following measures is not a triangle.

(iii) Base = 3 units

Altitude = 4 units

Hypotenuse = 5 units

= 3 + 4 > 5

= 7 > 5

the following measures is a triangle.

(iv) Base = 9 units

Altitude = 12 units

Hypotenuse = 15 units

= 9 + 12 > 15

= 21 > 15

the following measures is a triangle.

(v) Base = 5 units

Altitude = 12 units

Hypotenuse = 13 units

= 5 + 12 > 13

= 17 > 15

the following measures is a triangle.

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