Question

1. if △sde ~ △swt, find wt.
2. if △gfe ~ △ghj, find the value of x.
3. △xzw ~ △xyv, find the perimeter of △xzw

Explanation:

Step1: Use similarity - side ratio for problem 8

Since $\triangle SDE\sim\triangle SWT$, the ratios of corresponding sides are equal. So, $\frac{SD}{SW}=\frac{SE}{ST}=\frac{DE}{WT}$. We have $\frac{56}{5x + 3}=\frac{40}{4x-3}$. Cross - multiply: $56(4x - 3)=40(5x + 3)$.

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Then $WT=5x + 3=5\times12+3=63$.

Step2: Use similarity - side ratio for problem 9

Since $\triangle GFE\sim\triangle GHJ$, we have $\frac{FG}{GH}=\frac{EG}{GJ}$. So, $\frac{x + 6}{7.5}=\frac{12}{2x + 1}$. Cross - multiply: $(x + 6)(2x + 1)=12\times7.5$.

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$x = 4$ or $x=-\frac{21}{2}$. Since length cannot be negative, $x = 4$.

Step3: Use similarity - side ratio for problem 10

Since $\triangle XZW\sim\triangle XYV$, the ratio of corresponding sides is $\frac{XW}{XV}=\frac{XZ}{XY}=\frac{ZW}{YV}$. The ratio of similarity is $\frac{40}{32}=\frac{5}{4}$. The sides of $\triangle XYV$ are $30,28,32$. The sides of $\triangle XZW$ are $\frac{5}{4}\times30=\frac{150}{4}=37.5$, $\frac{5}{4}\times28 = 35$, $\frac{5}{4}\times32 = 40$. The perimeter of $\triangle XZW$ is $37.5+35 + 40=112.5$.

Answer:

1. $WT = 63$
2. $x = 4$
3. Perimeter of $\triangle XZW=112.5$