Question

Write a Pythagorean triplet whose one member is 35.

Answer 1

I hope this helped you a lot

Answer 2

In a Pythagorean Triplet, we have a base, height and hypotenuse.

Base ⇒ $\sf 2m$

Height ⇒ $\sf m^2-1$

Hypotenuse ⇒ $\sf m^2+1$

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Now, we have to find in which of the above does 35 go under.

Let's start with the base.

$\sf \rightarrow 2m = 35\\ \\ \rightarrow m = \frac{35}{2} \\ \\ \rightarrow m= 17.5$

∴ 35 is not the base.

Let's check with the height.

$\sf \rightarrow m^2-1 = 35 \\ \\ \rightarrow m^2 = 36 \\ \\ \rightarrow \sqrt{m^2} =6\\ \\ \rightarrow m = 6$

∴ 35 could be the height.

Let's check with the hypotenuse.

$\sf \rightarrow m^2+1 = 35 \\ \\ \rightarrow m^2 = 34$

∴ 35 is not the hypotenuse.

$\rule{300}{1}$

Now we know that the height is 35 and the value of 'm' is 6. Let's find the Pythagorean Triplet.

Base ⇒

$\sf \rightarrow 2m \\ \\ \rightarrow 2\times 6 \\ \\ \rightarrow 12$

∴The base is 12.

Height ⇒

$\sf \rightarrow m^2-1 \\ \\ \rightarrow 6^2-1\\ \\ \rightarrow 36-1\\ \\ \rightarrow 35$

∴The height is 35.

Hypotenuse ⇒

$\sf \rightarrow m^2+1\\ \\ \rightarrow 6^2+1 \\ \\ \rightarrow 36+1 \\ \\ \rightarrow 37$

∴The hypotenuse is 37.

$\rule{300}{1}$

∴The Pythagorean Triplet is ⇒ 12, 35 and 37.