Question

Use the Pythagorean Theorem to find the value of the hypotenuse.

a=3b=4c-? A) 10 B) 12 C) 5 D) 6 E) 4​

Answer 1

Answer:

a²= b²+ c²

Step-by-step explanation:

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Answer 2

Explanation:

We can solve this question by two methods, which I shall present.

$\textsf{\textbf{The unintended simple way:}}$

We know that in a Pythagorean triplet, there are three numbers: $\mathsf{2n, n^2-1, n^2+1}$.

In this question,

$\mathsf{4 =2\times2, 3=2^2-1}$.

Hence, n = 2.

Hence,

$\mathsf{n^2+1=2^2+1=4+1=5}$.

$\textsf{\textbf{The intended way:}}$

The Pythagoras theorem says that if three numbers form a Pythagorean triplet,

$\mathsf{c^2=a^2+b^2}$

$\mathsf{==>c^2=4^2+3^2}$

$\mathsf{==>c^2=16+9}$

$\mathsf{==>c^2=25}$

$\mathsf{==>c=\sqrt{25}}$

∴ $\mathsf{c=5}$

Answer: c = 5

I hope this helps. :D