Question

name: date: per: unit 6: similar triangles homework 5: parallel lines & proportional parts directions: solve for x. 1. this is a 2 - page document! 2. 3. 4. 5. 6. 7. find ce.

Explanation:

Step1: Use similarity of triangles

For similar - triangles, the ratios of corresponding sides are equal. For problem 1, if the two triangles are similar, then $\frac{x}{32}=\frac{9}{24}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{x}{32}=\frac{9}{24}$ gives $24x = 32\times9$.

Step3: Solve for x

$x=\frac{32\times9}{24}=\frac{288}{24}=12$.

Step1: Set up proportion

Since the two triangles are similar, we have $\frac{x + 5}{30}=\frac{20}{36}$.

Step2: Cross - multiply

Cross - multiplying gives $36(x + 5)=20\times30$.

Step3: Expand and solve

$36x+180 = 600$. Then $36x=600 - 180=420$. So $x=\frac{420}{36}=\frac{35}{3}\approx11.67$.

Step1: Set up proportion

Because of similar triangles, $\frac{x + 8}{20}=\frac{2x - 5}{22.5}$.

Step2: Cross - multiply

$22.5(x + 8)=20(2x - 5)$.

Step3: Expand

$22.5x+180 = 40x-100$.

Step4: Rearrange terms

$40x-22.5x=180 + 100$.

Step5: Solve for x

$17.5x=280$, so $x = 16$.

Step1: Set up proportion

From similar triangles, $\frac{4}{2x + 4}=\frac{3}{x + 7}$.

Step2: Cross - multiply

$4(x + 7)=3(2x + 4)$.

Step3: Expand

$4x+28 = 6x+12$.

Step4: Rearrange terms

$6x-4x=28 - 12$.

Step5: Solve for x

$2x=16$, so $x = 8$.

Answer:

1. $x = 12$

For problem 3: