Question

Pleas help me find the answer and show the work to this question

Answer 1

`Leg\ 1 = 8`

`Leg\ 2 = 15`

Explanation:

Given: See Attachment

Required

Determine the length of the legs

To do this, we apply Pythagoras theorem.

`Hyp^2 = Adj^2 + Opp^2`

In this case:

`17^2 = x^2 + (2x- 1)^2`

Open Bracket

`17^2 = x^2 + 4x^2- 2x-2x + 1`

`17^2 = 5x^2 - 4x + 1`

`289= 5x^2 - 4x + 1`

Collect Like Terms

`5x^2 - 4x + 1 - 289 = 0`

`5x^2 - 4x - 288 = 0`

Solving using quadratic formula:

`x = (-b\±√(b^2 - 4ac))/(2a)`

So:

`x = 8` or
`x = -7.2`

Since, x can't be negative, then:

`x = 8`

One of the leg is:

`Leg\ 1 = x`

`Leg\ 1 = 8`

`Leg\ 2 = 2x - 1`

`Leg\ 2 = 2*8 - 1`

`Leg\ 2 = 16 - 1`

`Leg\ 2 = 15`