Question

geometry
similar triangles assignment
set up the proportions needed to solve for x (the equation you would type into desmos).
1)
2)
3)
4)
5)
6)

Explanation:

Step1: Recall similar - triangles property

For similar triangles, the ratios of corresponding sides are equal.

Step2: Solve problem 1

Let the unknown side be $x$. The proportion is $\frac{12}{x}=\frac{2}{3}$, which can be written as $2x = 12\times3$.

Step3: Solve problem 2

Let the unknown side be $x$. The proportion is $\frac{x}{2}=\frac{3}{1}$, or $x=\frac{2\times3}{1}$.

Step4: Solve problem 3

Let the unknown side be $x$. The proportion is $\frac{6}{x}=\frac{5}{8}$, or $5x = 6\times8$.

Step5: Solve problem 4

Let the unknown side be $x$. The proportion is $\frac{24 - 4}{x}=\frac{24}{30}$, or $24x=(24 - 4)\times30$.

Step6: Solve problem 5

Let the unknown side be $x$. The proportion is $\frac{x}{24}=\frac{15}{18}$, or $18x = 15\times24$.

Step7: Solve problem 6

Let the unknown side be $x$. The proportion is $\frac{15 - x}{15}=\frac{8}{12}$, or $12\times(15 - x)=15\times8$.

Answer:

1. $2x = 12\times3$
2. $x=\frac{2\times3}{1}$
3. $5x = 6\times8$
4. $24x=(24 - 4)\times30$
5. $18x = 15\times24$
6. $12\times(15 - x)=15\times8$