Similar Triangle Construction

KLM triangle on sides k = 5.4 cm. L = 6 cm, m = 6.6 cm.
Construct a triangle K 'L'M 'for which the following holds: ∆KLM ~ ∆K 'L'M' and m '= 9.9 cm

Final Answer:

k₁ =  8.1 cm
l₁ =  9 cm
m₁ =  9.9 cm

Step-by-step explanation:

$$\begin{gathered} k=5.4\text{cm} \\ l=6\text{cm} \\ m=6.6\text{cm} \\ {m}_1=9.9\text{cm} \\ q=\frac{m_1}{m}=\frac{9.9}{6.6}=\frac{3}{2}=1.5 \\ {k}_1=q\cdot k=1.5\cdot 5.4=\frac{81}{10}\text{cm}=8.1\text{cm} \end{gathered}$$

$l_1=q\cdot l=\frac{3}{2}\cdot 6=\frac{3\cdot 6}{2}=\frac{18}{2}=9\text{cm}$

$m_1=q\cdot m=1.5\cdot 6.6=9.9\text{cm}$

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