Question

solve for x. the triangles in each pair are similar.
17)
18)
19)
20)

Explanation:

17) Step1: Set up proportion for similar triangles

$\frac{11x-4}{50} = \frac{70}{60}$

17) Step2: Cross-multiply to eliminate fractions

$60(11x-4) = 70 \times 50$

17) Step3: Simplify both sides

$660x - 240 = 3500$

17) Step4: Isolate the variable term

$660x = 3500 + 240$
$660x = 3740$

17) Step5: Solve for x

$x = \frac{3740}{660} = \frac{17}{3} \approx 5.67$

18) Step1: Set up proportion for similar triangles

$\frac{11x+11}{21} = \frac{77}{30}$

18) Step2: Cross-multiply to eliminate fractions

$30(11x+11) = 77 \times 21$

18) Step3: Simplify both sides

$330x + 330 = 1617$

18) Step4: Isolate the variable term

$330x = 1617 - 330$
$330x = 1287$

18) Step5: Solve for x

$x = \frac{1287}{330} = \frac{39}{10} = 3.9$

19) Step1: Set up proportion for similar triangles

$\frac{-4+4x}{64} = \frac{27}{72}$

19) Step2: Simplify the right-hand side

$\frac{-4+4x}{64} = \frac{3}{8}$

19) Step3: Cross-multiply to eliminate fractions

$8(-4+4x) = 3 \times 64$

19) Step4: Simplify both sides

$-32 + 32x = 192$

19) Step5: Isolate the variable term

$32x = 192 + 32$
$32x = 224$

19) Step6: Solve for x

$x = \frac{224}{32} = 7$

20) Step1: Set up proportion for similar triangles

$\frac{5x+11}{18} = \frac{88}{24}$

20) Step2: Simplify the right-hand side

$\frac{5x+11}{18} = \frac{11}{3}$

20) Step3: Cross-multiply to eliminate fractions

$3(5x+11) = 11 \times 18$

20) Step4: Simplify both sides

$15x + 33 = 198$

20) Step5: Isolate the variable term

$15x = 198 - 33$
$15x = 165$

20) Step6: Solve for x

$x = \frac{165}{15} = 11$

Answer:

1. $x = \frac{17}{3}$
2. $x = \frac{39}{10}$
3. $x = 7$
4. $x = 11$