4
If two triangles are similar, corresponding sides are in proportion. So, we have
[tex] \dfrac{17.5}{14} = \dfrac{2y}{y+3}[/tex]
Multiply both sides by [tex]14(y+3)[/tex] to get
[tex] 17.5(y+3) = 28y [/tex]
Expand the left hand side:
[tex] 17.5y + 52.5 = 28y [/tex]
Subtract 17.5y from both sides:
[tex] 52.5 = 10.5y [/tex]
Divide both sides by 10.5:
[tex] y = 5 [/tex]
8
Given the ratio
[tex] \dfrac{x}{y} = \dfrac{4}{11} [/tex]
we can deduce
[tex] x = \dfrac{4}{11}y[/tex]
The perimeter of the rectangle is given by
[tex] 2x+2y = 2\cdot \dfrac{4}{11}y + 2y = \dfrac{30}{11}y = 650 \iff y = \dfrac{715}{3} [/tex]
Now we can deduce the value for x:
[tex] x = \dfrac{4}{11}\cdot\dfrac{715}{3} = \dfrac{260}{3}[/tex]
