Question

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

Answer 1

Answer:

$Leg\ 1 = 8$

$Leg\ 2 = 15$

Step-by-step 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:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

So:

$x = 8$ or $x = -7.2$

Since, x can't be negative, then:

$x = 8$

One of the leg is:

$Leg\ 1 = x$

$Leg\ 1 = 8$

$Leg\ 2 = 2x - 1$

$Leg\ 2 = 2*8 - 1$

$Leg\ 2 = 16 - 1$

$Leg\ 2 = 15$