Question

find the value of x in each figure: (1) (2) (3)

Explanation:

Step1: Assume similar - shaped figures

For similar - shaped figures, the ratios of corresponding sides are equal.

(1)

Assume the two trapezoids are similar. Then, using the ratio of corresponding sides:
We have $\frac{x}{11}=\frac{11}{7}$. Cross - multiply to get $7x = 11\times11$.
$7x=121$. Then $x=\frac{121}{7}\approx17.29$.

(2)

Assume the two similar - shaped figures (perhaps similar parallelograms or trapezoids). Using the ratio of corresponding sides:
$\frac{x}{10}=\frac{10}{3x}$. Cross - multiply to get $3x^{2}=100$. Then $x^{2}=\frac{100}{3}$, and $x=\pm\sqrt{\frac{100}{3}}=\pm\frac{10}{\sqrt{3}}$. Since $x$ represents a length, we take the positive value $x = \frac{10}{\sqrt{3}}=\frac{10\sqrt{3}}{3}\approx5.77$.

(3)

Assume the two figures are similar. Then, using the ratio of corresponding sides:
$\frac{5x + 12}{5x}=\frac{5x}{3x}$. Simplify the right - hand side: $\frac{5x}{3x}=\frac{5}{3}$.
Cross - multiply the left - hand side ratio: $3(5x + 12)=25x$.
Expand: $15x+36 = 25x$.
Subtract $15x$ from both sides: $36=25x - 15x$.
$10x = 36$, so $x=\frac{36}{10}=3.6$.

Answer:

(1) $x=\frac{121}{7}$
(2) $x=\frac{10\sqrt{3}}{3}$
(3) $x = 3.6$