Question

The figures in each pair are similar. Find the value of each variable. Show your work.

Answer 1

When a pair of figure is similar, it means the lengths have a scale factor. So we have to find what times 8 gives 16, which is the length if the bigger rectangle. 8×2=16, so we have to use the scale factor, which is 2, to multiply by the other length of the rectangle. 2×2=4, so x=4.
Next question is basically like the first one, but you have to divide instead. 12÷4=3, and so 8×3=24, so y=24. 18÷3=6, so x=6. Last one, 6÷4= 1.5. 8÷1.5=5.3 and 7÷1.5=4.6, so x=4.6 and y=5.3

Answer 2

We know that the figures in each pair are similar and that x,y>0, so:

The rectangle:
$\frac{16}{8}=\frac{x}{2}$
$2=\frac{x}{2}\quad |\cdot 2$
$4=x$

The triangle I:
$\frac{y}{12}=\frac{8}{4}$
$\frac{y}{12}=2\quad |\cdot 12$
$y=24$

$\frac{12}{4}=\frac{18}{x}$
$3=\frac{18}{x}\quad |\cdot x$
$3x=18\quad |:3$
$x=6$

The triangle II:
$\frac{8}{6}=\frac{y}{4}$
$32=6y\quad |:6$
$y=5\frac{1}{3}$

$\frac{6}{4}=\frac{7}{x}$
$\frac{3}{2}=\frac{7}{x}$
$3x=14$
$x=4\frac{2}{3}$

:)