Question

Please help

Answer 1

4

If two triangles are similar, corresponding sides are in proportion. So, we have

$\dfrac{17.5}{14} = \dfrac{2y}{y+3}$

Multiply both sides by $14(y+3)$ to get

$17.5(y+3) = 28y$

Expand the left hand side:

$17.5y + 52.5 = 28y$

Subtract 17.5y from both sides:

$52.5 = 10.5y$

Divide both sides by 10.5:

$y = 5$

8

Given the ratio

$\dfrac{x}{y} = \dfrac{4}{11}$

we can deduce

$x = \dfrac{4}{11}y$

The perimeter of the rectangle is given by

$2x+2y = 2\cdot \dfrac{4}{11}y + 2y = \dfrac{30}{11}y = 650 \iff y = \dfrac{715}{3}$

Now we can deduce the value for x:

$x = \dfrac{4}{11}\cdot\dfrac{715}{3} = \dfrac{260}{3}$