Question

Reason quantitatively. The two rectangles shown
are similar. What is the value of x

Answer 1

Two shapes are similar if the ratio of the lengths of their corresponding sides are equal.

Both shapes given in the question are rectangles, therefore, one pair of opposite sides is longer than the other.

We can find the ratio for the bigger rectangle since it has all the values complete and then compare this ratio to the smaller rectangle to find the value of the unknown side.

The ratio of the longer side to the shorter side for the bigger rectangle is

`\begin{gathered} (16)/(2) \\ =8 \end{gathered}`

Therefore, for the smaller rectangle, the ratio of the longer side to the shorter side is

`(4)/(x)=8`

Solving for x, we have

`\begin{gathered} x=(4)/(8) \\ x=0.5 \end{gathered}`

The value for x is 0.5.