Question

find the length of cn in the triangle below where \\(\overline{mn}\parallel\overline{ac}\\).
4.
a 8
24
4.5
13.5
5.
in the diagram below of \\(\triangle act\\), \\(be\parallel\overline{at}\\). if \\(cb = 3\\), \\(ca = 10\\) and \\(ce = 6\\), what is the length of \\(\overline{et}\\)?
a 26
5
20
14

Explanation:

Problem 4

Step1: Apply Basic Proportionality Theorem

Since $\overline{MN} \parallel \overline{AC}$, the sides are proportional:
$\frac{BM}{MA} = \frac{BN}{NC}$

Step2: Substitute given values

$\frac{12}{18} = \frac{16}{3x}$

Step3: Simplify and solve for $x$

Cross-multiply: $12 \times 3x = 18 \times 16$
$36x = 288$
$x = \frac{288}{36} = 8$

Step4: Calculate length of $CN$

$CN = 3x = 3 \times 8$

Step1: Apply Basic Proportionality Theorem

Since $\overline{BE} \parallel \overline{AT}$, the sides are proportional:
$\frac{CB}{BA} = \frac{CE}{ET}$

Step2: Calculate length of $BA$

$BA = CA - CB = 10 - 3 = 7$

Step3: Substitute values and solve for $ET$

$\frac{3}{7} = \frac{6}{ET}$
Cross-multiply: $3 \times ET = 6 \times 7$
$3ET = 42$
$ET = \frac{42}{3}$

Answer:

B. 24

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Problem 5