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

Question

asked Dec 4, 2021 142k views

1 Answer

Jmosbech · Answer 1 · 2021-12-11T17:23:25+0000

Answer:

$Leg\ 1 = 8$

$Leg\ 2 = 15$

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:

$Leg\ 1 = x$

$Leg\ 1 = 8$

$Leg\ 2 = 2x - 1$

$Leg\ 2 = 2*8 - 1$

$Leg\ 2 = 16 - 1$

$Leg\ 2 = 15$