Answer:
1. [tex]\dfrac{44}{13}=3\dfrac{5}{13}[/tex]
2. 9.6
3. 0
Step-by-step explanation:
Thales’ Theorem: If arms of an angle are cut by parallel straight lines, then the ratio of the lengths of the line segments obtained on one arm are equal to the corresponding segments obtained on the second arm.
1. By Thales's theorem,
[tex]\dfrac{9}{4}=\dfrac{11-x}{x}\\ \\9x=4(11-x)\ [\text{Cross multiply}]\\ \\9x=44-4x\\ \\9x+4x=44\\ \\13x=44\\ \\x=\dfrac{44}{13}[/tex]
2. By Thales's theorem,
[tex]\dfrac{8}{12}=\dfrac{x}{24-x}\\ \\12x=8(24-x)\ [\text{Cross multiply}]\\ \\12x=192-8x\\ \\12x+8x=192\\ \\20x=192\\ \\x=9.6[/tex]
3. By Thales's theorem,
[tex]\dfrac{4x}{5x}=\dfrac{4x-8}{6x-10}\\ \\\dfrac{4}{5}=\dfrac{4x-8}{6x-10}\\ \\5(4x-8)=4(6x-10)\ [\text{Cross multiply}]\\ \\20x-40=24x-40\\ \\20x=24x\\ \\4x=0\\ \\x=0[/tex]
