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liberstina [14]
3 years ago
14

Part A Prove that when x > 1, a triangle with side lengths a = x2 − 1, b = 2x, and c = x2 + 1 is a right triangle. Use the Py

thagorean theorem and the given side lengths to create an equation. Use the equation to show that this triangle follows the rule describing right triangles. Explain your steps.
Mathematics
1 answer:
Nataly [62]3 years ago
7 0

Step-by-step explanation:

Given : A triangle with side lengths a = x^2-1, b = 2x, \text{ and } c = x^2 + 1

To find : Prove that when x > 1, it is a right triangle. Use the Pythagorean theorem and the given side lengths to create an equation. Use the equation to show that this triangle follows the rule describing right triangles. Explain your steps ?

Solution :

For right triangle the Pythagorean theorem is to be satisfied.

i.e. c^2=a^2+b^2

Here, a = x^2-1, b = 2x, \text{ and } c = x^2 + 1

Substitute the values,

(x^2+1)^2=(x^2-1)^2+(2x)^2

x^4+1+2x^2=x^4+1-2x^2+4x^2

x^4+1+2x^2=x^4+1+2x^2

LHS=RHS

It is a right triangle.

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