Answer:
x could be 9.2, 10 or 10.8.
Explanation:
If the triangle to be formed would be an isosceles, then:
DE = x = 10.
If the triangle is a right angled with CD = 10 as the hypotenuse. Applying Pythagoras theorem, we have:
[tex]10^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]
100 = [tex]x^{2}[/tex] + 16
100 - 16 = [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 84
x = [tex]\sqrt{84}[/tex]
= 9.1652
≅ 9.2
If the triangle is a right angled with DE = x as the hypotenuse, then:
[tex]x^{2}[/tex] = [tex]10^{2}[/tex] + [tex]4^{2}[/tex]
= 100 + 16
= 116
x = [tex]\sqrt{116}[/tex]
= 10.7703
x = 10.8
