Question

solve for x.
7)
8)
9)
10)
11)
12)

Explanation:

Step1: Use similar - triangle property for problem 7

If two triangles are similar, the ratios of their corresponding sides are equal. Given $\frac{3x}{9}=\frac{4}{3}$. Cross - multiply to get $3x\times3 = 9\times4$.
$9x=36$

Step2: Solve for x

Divide both sides of the equation $9x = 36$ by 9.
$x = 4$

Step3: Use similar - triangle property for problem 8

The two triangles are similar, so $\frac{2x - 11}{20}=\frac{12}{15}$. Cross - multiply: $15\times(2x - 11)=12\times20$.
$30x-165 = 240$

Step4: Solve for x in problem 8

Add 165 to both sides: $30x=240 + 165=405$. Then divide by 30, $x = 13.5$

Step5: Use similar - triangle property for problem 10

Since the triangles are similar, $\frac{5x + 3}{9}=\frac{8}{4}$. Cross - multiply: $4\times(5x + 3)=9\times8$.
$20x+12 = 72$

Step6: Solve for x in problem 10

Subtract 12 from both sides: $20x=72 - 12 = 60$. Divide by 20, $x = 3$

Step7: Use similar - triangle property for problem 12

The triangles are similar, so $\frac{x + 4}{6}=\frac{5}{3}$. Cross - multiply: $3\times(x + 4)=6\times5$.
$3x+12 = 30$

Step8: Solve for x in problem 12

Subtract 12 from both sides: $3x=30 - 12 = 18$. Divide by 3, $x = 6$

Answer:

For problem 7: $x = 4$
For problem 8: $x = 13.5$
For problem 10: $x = 3$
For problem 12: $x = 6$