$100 \%$ $\newline$ The two pentagons shown are similar. $\newline$ What is the value of $x$ ? $\newline$ A. $6 \mathrm{~cm}$ $\newline$ B. $9 \mathrm{~cm}$ $\newline$ C. $12 \mathrm{~cm}$ $\newline$ D. $14 \mathrm{~cm}$

Full solution

100 \%

\newline

The two pentagons shown are similar.

\newline

What is the value of

x

\newline

6 \mathrm{~cm}

\newline

9 \mathrm{~cm}

\newline

12 \mathrm{~cm}

\newline

14 \mathrm{~cm}

Define Ratios: Since the pentagons are similar, the ratio of corresponding sides is constant. Let's call the sides of the smaller pentagon ' $a$ ' and the sides of the larger pentagon ' $b$ '. The ratio $\frac{a}{b}$ should be equal for all corresponding sides.
Identify Corresponding Sides: We need to find the given sides that correspond to ' $x$ ' in the larger pentagon. Let's say the side corresponding to ' $x$ ' in the smaller pentagon is ' $y$ '. So, the ratio $\frac{x}{y}$ should be equal to the ratio of any other two corresponding sides.
Use Given Side Lengths: Let's assume the problem provides the lengths of one pair of corresponding sides. For example, if a side of the smaller pentagon is $3\,\text{cm}$ and the corresponding side of the larger pentagon is $4.5\,\text{cm}$ , then the ratio is $\frac{4.5}{3}$ or $1.5$ .
Apply Ratio to Find $x$ : Now, we apply this ratio to find ' $x$ '. If ' $y$ ' is a side of the smaller pentagon, then $x = 1.5 \times y$ . But we need the actual values to calculate ' $x$ '.
Need Additional Information: Since the problem doesn't give us the actual lengths of the sides, we can't calculate $x$ without more information. We need either the length of $y$ or another pair of corresponding sides to find the ratio.