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:

`(16)/(8)=(x)/(2)`

`2=(x)/(2)\quad |\cdot 2`

`4=x`

The triangle I:

`(y)/(12)=(8)/(4)`

`(y)/(12)=2\quad |\cdot 12`

`y=24`


`(12)/(4)=(18)/(x)`

`3=(18)/(x)\quad |\cdot x`

`3x=18\quad |:3`

`x=6`

The triangle II:

`(8)/(6)=(y)/(4)`

`32=6y\quad |:6`

`y=5(1)/(3)`


`(6)/(4)=(7)/(x)`

`(3)/(2)=(7)/(x)`

`3x=14`

`x=4(2)/(3)`

:)