# Identify, with reason, which of the following are Pythagorean triplets.(1) (24,70,74) (2) (10,24,27) (3) (11,60,61)

Given:

Given triplets are

(1) (24,70,74)

(2) (10,24,27)

(3) (11,60,61)

To do:

To check whether the given triplets are Pythagorean Triplets.

Solution:

According to Pythagorean triplet:

The square of the largest number is equal to the sum of the square of the other two numbers.

(a) Here, $74^2= 5476$, $70^2=4900$, $24^2=576$

$\therefore 70^2+24^2=4900+576=5476$

$\Rightarrow 74^2=70^2+24^2$

Hence they form a Pythagorean triplet.

(b) Here, $27^2= 729$, $24^2=576$, $10^2=100$

$\therefore 24^2+10^2=576+100=676$

$\Rightarrow 27^2≠24^2+10^2$

Hence they do not form a Pythagorean triplet.

(c) Here, $61^2= 3721$, $60^2=3600$, $11^2=121$

$\therefore 60^2+11^2=3600+121=3721$

$\Rightarrow 61^2=60^2+11^2$

Hence they form a Pythagorean triplet.

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Updated on: 10-Oct-2022

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