Answer:
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 15[/tex]
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
In this case:
[tex]17^2 = x^2 + (2x- 1)^2[/tex]
Open Bracket
[tex]17^2 = x^2 + 4x^2- 2x-2x + 1[/tex]
[tex]17^2 = 5x^2 - 4x + 1[/tex]
[tex]289= 5x^2 - 4x + 1[/tex]
Collect Like Terms
[tex]5x^2 - 4x + 1 - 289 = 0[/tex]
[tex]5x^2 - 4x - 288 = 0[/tex]
Solving using quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
So:
[tex]x = 8[/tex] or [tex]x = -7.2[/tex]
Since, x can't be negative, then:
[tex]x = 8[/tex]
One of the leg is:
[tex]Leg\ 1 = x[/tex]
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 2x - 1[/tex]
[tex]Leg\ 2 = 2*8 - 1[/tex]
[tex]Leg\ 2 = 16 - 1[/tex]
[tex]Leg\ 2 = 15[/tex]
