Triangle LMN is similar to triangle XYZ, where vertex L corresponds to vertex X, vertex M … — SAT

Triangle $LMN$ is similar to triangle $XYZ$ , where vertex $L$ corresponds to vertex $X$ , vertex $M$ corresponds to vertex $Y$ , and vertex $N$ corresponds to vertex $Z$ . The length of side $LM$ is $5$ , the length of side $XY$ is $15$ , and the length of side $YZ$ is $24$ . What is the length of side $MN$ ?

8Cevap
B
72
C
14
D
9

Cevap

The correct answer is 8. Similar triangles have corresponding side lengths that are proportional. The ratio of the length of side

LM

to the length of its corresponding side

XY

5

15

, which simplifies to

1

3

. Since side

MN

corresponds to side

YZ

, the ratio of the length of side

MN

to the length of side

YZ

must also be

1

3

. Setting up the proportion

\frac{1}{3} = \frac{MN}{24}

and solving for the length of side

MN

yields

8

Adım Adım Çözüm

Identify corresponding sides of the similar triangles and set up a proportion.

\frac{LM}{XY} = \frac{MN}{YZ}

Similar triangles have proportional corresponding side lengths.

Substitute the given values into the proportion.

\frac{5}{15} = \frac{MN}{24}

The given lengths are

LM = 5

XY = 15

, and

YZ = 24

Simplify the fraction and solve for

MN

MN = 8

\frac{5}{15}

simplifies to

\frac{1}{3}

. Multiplying both sides of

\frac{1}{3} = \frac{MN}{24}

24

yields

MN = 8

Anahtar Kavram

Triangle Similarity and Proportional Side Lengths

Alternatif Yöntem

Find the scale factor from triangle

LMN

to triangle

XYZ

by dividing

XY

LM

15 / 5 = 3

. Since triangle

XYZ

3

times larger than triangle

LMN

, divide the length of side

YZ

3

to find the length of corresponding side

MN

24 / 3 = 8

Tahmini Süre:45s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Konular

Bu konudan daha fazla soru