Question

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. What is the value of X in simplest radical form?

X=_____

Answer 1

X=97

Explanation:

The formula for the Pythagorean Theorem is:

`√(a^2+b^2)=c`

Now,

A=65

B=72

72x72=5184

65x65=4225

4225+5184=9409

Last,

Take the square root of 9409.

The square root is 97.

Therefore, the hypotenuse is 97.

To check, use the equation:

`a^2+b^2=c^2`

A=65

B=72

C=97

72x72=5184

65x65=4225

97x97=9409

5184+4225=9409

9409=9409

Therefore, the missing side, which is the hypotenuse, is 97.

Answer 2

97

Explanation:

Given:

• Opposite = 65
• Adjacent = 72
• Hypotenuse = x

Definition:

• Opposite is a perpendicular/vertical side.
• Adjacent is a horizontal side, by adding opposite and adjacent together, you have formed a right angle.
• Hypotenuse is the longest side of all which is the side that’s opposite of the right angle.

To find:

• Value of x

Pythagorean Theorem:

`\displaystyle \large{a^2+b^2=c^2}`

Determine:

• a = opposite
• b = adjacent
• c = hypotenuse

Note:

• a and b can swap each other so you can determine a = adjacent and b = opposite instead of a = opposite and b = adjacent. This is because of addition property.
• The exception is value of c - ‘c’ cannot be changed and must be hypotenuse.

Therefore, substitute given information in:

`\displaystyle \large{65^2+72^2=x^2}`

Evaluate:

`\displaystyle \large{4225+5184=x^2}\\\displaystyle \large{9409=x^2}`

Square Root both sides:

`\displaystyle \large{√(9409) = √(x^2)}`

Cancel the squared x, add plus-minus:

`\displaystyle \large{\pm √(9409) = x}`

Simplify the surd:

`\displaystyle \large{\pm 97 = x}`

However, side length is a scalar value so it cannot be negative nor have negative values. Therefore:

`\displaystyle \large{x=97}`

Hence, the value of x is 97