Question

What is the value of x in the diagram?

Answer 1

5

Explanation:

Given is a right angled triangle.

Therefore, by Pythagoras theorem:

`{(2x + 3)}^(2) = {x}^(2) + {(2x + 2)}^(2) \\ 4 {x}^(2) + 9 + 12x = {x}^(2) + 4 {x}^(2) + 4 + 8x \\ 9 + 12x = {x}^(2) + 4 + 8x \\ {x}^(2) + 4 + 8x - 12x - 9 = 0 \\ {x}^(2) - 4x - 5 = 0 \\ ({x}^(2) - 4x + 4 )- 4 - 5 = 0 \\ {(x - 2)}^(2) - 9 = 0 \\ {( x - 2)}^(2) = 9 \\ x - 2 = \pm \: √(9) \\ x - 2 = \pm 3 \\ x = 2 \pm 3 \\ x = 2 + 3 \: \: or \: \: x = 2 - 3 \\ x = 5 \: \: or \: \: x = - 1 \\ \because \: x \: can \: not \: be \: negative \\ \therefore \: x \\eq \: - 1 \\ \therefore \: x = 5`