Question

Form an equation. Find the value of x which is compatible with the given diagram.

Answer 1

Answer:

I am thinking it's right

Answer 2

ANSWER = 6 , 8 , 10

$\sf\ since \: this \: is \: a \: right \: triangle \:$

$\sf \boxed{according \: to \: pythagorean \: theorom}$

$\sf \boxed{base {}^{2} + {altitude}^{2} = hypotenuse \: {}^{2} }$

$(x + 3) {}^{2} + (x + 1) {}^{2} = (x + 5) {}^{2}$

${x}^{2} + 6x + 9 + {x}^{2} + 2x + 1 = (x + 5) {}^{2}$

$\implies \: 2 {x}^{2} + 8x + 10 = {x}^{2} + 10x + 25$

$\implies \: 2 {x}^{2} - {x}^{2} + 8x - 10x + 10 - 25 = 0$

$\implies {x}^{2} - 2x - 15 = 0$

$\implies \: (x - 5)(x + 3)$

$\implies \: 5 \: and \: \: - 3$

$\sf\ \: since \: distance \: cannot \: be \: negative \: value \: of \: x \:$

$\sf \: will \: be \: 5$

Sides of the traingle

x + 1 = 6

x + 3 = 8

x + 5 = 10