Question

1. $jklm \sim qrsp$

angles sides

using similar figures to solve for missing measures.

1. if the figures below are similar with a scale factor of 2:3, find the value of $x$.
2. if the figures below are similar with a scale factor of 6:5, find the value of $x$.
3. if $\triangle abc \sim \triangle def$, find the value of $x$.
4. if $pqrs \sim wxyz$, find the value of $x$.
5. if $\triangle agm \sim \triangle kxd$, find the value of $x$.
6. if $\triangle tly \sim \triangle chk$, find the value of $x$.

Explanation:

Problem 4

Step1: Set up scale proportion

$\frac{2}{3} = \frac{42}{x}$

Step2: Cross-multiply to solve

$2x = 42 \times 3$
$2x = 126$
$x = \frac{126}{2} = 63$

Problem 5

Step1: Set up scale proportion

$\frac{6}{5} = \frac{x}{28}$

Step2: Cross-multiply to solve

$5x = 28 \times 6$
$5x = 168$
$x = \frac{168}{5} = 33.6$

Problem 6

Step1: Find scale factor

$\text{Scale factor} = \frac{28}{25}$

Step2: Set up proportion for $x$

$\frac{x}{20} = \frac{28}{25}$

Step3: Solve for $x$

$x = 20 \times \frac{28}{25} = \frac{560}{25} = 22.4$

Problem 7

Step1: Find scale factor

$\text{Scale factor} = \frac{75}{40} = \frac{15}{8}$

Step2: Set up proportion for $x$

$\frac{x}{32} = \frac{15}{8}$

Step3: Solve for $x$

$x = 32 \times \frac{15}{8} = 60$

Problem 8

Step1: Set up proportion of sides

$\frac{32}{x+3} = \frac{36}{x+6}$

Step2: Cross-multiply to simplify

$32(x+6) = 36(x+3)$
$32x + 192 = 36x + 108$

Step3: Rearrange to solve for $x$

$192 - 108 = 36x - 32x$
$84 = 4x$
$x = \frac{84}{4} = 21$

Problem 9

Step1: Set up proportion of sides

$\frac{25}{10} = \frac{4x-1}{x+5}$

Step2: Simplify and cross-multiply

$\frac{5}{2} = \frac{4x-1}{x+5}$
$5(x+5) = 2(4x-1)$
$5x + 25 = 8x - 2$

Step3: Rearrange to solve for $x$

$25 + 2 = 8x - 5x$
$27 = 3x$
$x = \frac{27}{3} = 9$

Answer:

1. $x=63$
2. $x=33.6$
3. $x=22.4$
4. $x=60$
5. $x=21$
6. $x=9$