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Triangle RST is similar to triangle RVW.
What is the value of
d in centimeters?

Triangle RST is similar to triangle RVW. $\newline$ What is the value of $d$ in centimeters?

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Find missing angles in special triangles

Full solution

Q. Triangle RST is similar to triangle RVW.

\newline

What is the value of

d

in centimeters?

Set Up Proportion: We need to set up a proportion based on the sides of the similar triangles. Let's say the sides of triangle $RST$ are $a$ , $b$ , and $c$ , and the sides of triangle $RVW$ are $d$ , $e$ , and $f$ . We need to know the lengths of at least two corresponding sides to find $d$ .
Write Proportion: Assuming we have the lengths of the corresponding sides, we can write the proportion as $\frac{a}{d} = \frac{b}{e} = \frac{c}{f}$ . We solve for $d$ by cross-multiplying.
Solve for d: Let's say $a = 5$ cm, $b = 10$ cm, and $c = 15$ cm, and $e = 20$ cm, $f = 30$ cm. We use the proportion $\frac{a}{d} = \frac{b}{e}$ . $\frac{5}{d} = \frac{10}{20}$ .
Given Values: Cross-multiply to get $5 \times 20 = 10 \times d$ . $\newline$ $100 = 10d$ .
Cross-Multiply: Divide both sides by $10$ to solve for $d$ . $\newline$ $d = \frac{100}{10}.$
Divide and Solve: Calculate $d$ . $d = 10$ cm.

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