Question

solve for x. the triangles in each pair are similar.

1. triangle srt with side sr = 11x - 4, st = 70; triangle bdc with side bd = 60, dc = 50
2. triangle abc with side ab = 77, bc = 11x + 11; triangle def with side de = 30, ef = 21
3. a triangle with a line segment creating a smaller similar triangle: the larger triangle has side length 96, the smaller has 36; the base of the larger is 72, the smaller is 27; the left side of the larger is 64, the smaller is -4 + 4x
4. triangle vwu with side vw = 88, vu = 5x + 11; triangle stu with side st = 24, su = 18

Explanation:

Step1: Set up proportion for Q17

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

Step2: Simplify right-hand side

$\frac{11x-4}{60} = \frac{7}{5}$

Step3: Cross-multiply to solve for x

$5(11x-4) = 7\times60$
$55x - 20 = 420$
$55x = 440$
$x = \frac{440}{55} = 8$

Step4: Set up proportion for Q18

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

Step5: Simplify and cross-multiply

$77\times21 = 30(11x+11)$
$1617 = 330x + 330$
$330x = 1617 - 330 = 1287$
$x = \frac{1287}{330} = 3.9$ or $\frac{99}{25}$

Step6: Set up proportion for Q19

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

Step7: Simplify right-hand side

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

Step8: Cross-multiply to solve for x

$8(-4+4x) = 3\times64$
$-32 + 32x = 192$
$32x = 224$
$x = \frac{224}{32} = 7$

Step9: Set up proportion for Q20

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

Step10: Simplify right-hand side

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

Step11: Cross-multiply to solve for x

$3(5x+11) = 11\times18$
$15x + 33 = 198$
$15x = 165$
$x = \frac{165}{15} = 11$

Answer:

1. $x=8$
2. $x=\frac{99}{25}$ or $x=3.9$
3. $x=7$
4. $x=11$