Question

Solve for x. Choose the best simplified radical answer where applicable. NO LINKS!!

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Answer 1

d)
`\sf x=10`

Explanation:

Pythagoras' Theorem:
`\sf a^2+b^2=c^2`

(where
`\sf a` and
`\sf b` are the legs, and
`\sf c` is the hypotenuse, of a right triangle)

Given:

• 
  `\sf a=4`
• 
  `\sf b=x`
• 
  `\sf c=2√(29)`

Substituting these values into the equation and solving for
`\sf x`:

`\sf \implies 4^2+x^2=(2√(29))^2`

`\sf \implies 16+x^2=116`

`\sf \implies x^2=116-16`

`\sf \implies x^2=100`

`\sf \implies x=\pm √(100)`

`\sf \implies x=\pm10`

Since distance is positive,
`\sf x=10` only

Therefore, the answer is d)
`\sf x=10`.

Answer 2

d. x = 10 (the correct answer is marked)

Explanation:

The Pythagorean theorem tells you the sum of the squares of the sides of a right triangle is the square of the hypotenuse.

x² +4² = (2√29)²

x² +16 = 116 . . . compute the squares

x² = 100 . . . . subtract 16

x = 10 . . . . take the square root