Find the exact value of x.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

This is a special right triangle, called a 45˚-45˚-90˚.

In a 45-45-90 triangle the sides opposite 45˚ must be equal.  The ratios of the sides are 1:1:`sqrt(2).`

Since the hypotenuse is 5, to find the length of x, we would divide by `sqrt(2).`

`:. 5/sqrt(2)` Must rationalize the denominator.

`5/sqrt(2)*sqrt(2)/sqrt(2) = (5sqrt(2))/2`

The solution for x is `(5sqrt(2))/2.`

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

This is an isosceles right triangle (45-45-90), where the two legs are equal and equal to

leg=leg=hypotenuse/`sqrt2`

Thus `x=5/sqrt2`

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial