Look at the picture.
Use the Pythagorean theorem to solve h:
[tex]h^2+5^2=7^2[/tex]
[tex]h^2+25=49[/tex] subtract 25 from both sides
[tex]h^2=24\to h=\sqrt{24}[/tex]
ΔADC and ΔCDB are similar. Therefore the sides are in proportion:
[tex]\dfrac{h}{5}=\dfrac{x}{h}[/tex] cross multiply
[tex]5x=h^2[/tex] put the value of h
[tex]5x=(\sqrt{24})^2[/tex]
[tex]5x=24[/tex] divide both sides by 5
[tex]x=4.8[/tex]
y = 5 + x → y = 5 + 4.8 = 9.8
Answer: y = 9.8
Or other method. ΔADC and ΔACB are similar. Therefore the sides are in proportion:
[tex]\dfrac{y}{7}=\dfrac{7}{5}[/tex] multiply both sides by 7
[tex]y=\dfrac{49}{5}\\\\\boxed{y=9.8}[/tex]
