Question

1. pentagon fghjk is similar to pentagon mpqst.

(diagrams of two pentagons: fghjk with side kf = 6 cm, jh = 9 cm; mpqst with side tm = 9 cm, sq = x cm)
what is the value of x?
a. 13.5
b. 12
c. 9.5
d. not here
7th grade fall semester final

Explanation:

Step1: Identify Corresponding Sides

In similar pentagons, corresponding sides are proportional. Side \( KF = 6 \, \text{cm} \) in pentagon \( FGHJK \) corresponds to side \( TM = 9 \, \text{cm} \) in pentagon \( MPQST \). Side \( JH = 9 \, \text{cm} \) in \( FGHJK \) corresponds to side \( SQ = x \, \text{cm} \) in \( MPQST \).

Step2: Set Up Proportion

Let the ratio of corresponding sides be \( \frac{\text{Side in } FGHJK}{\text{Side in } MPQST} \). So, \( \frac{KF}{TM} = \frac{JH}{SQ} \), which is \( \frac{6}{9} = \frac{9}{x} \).

Step3: Solve for \( x \)

Cross - multiply: \( 6x = 9\times9 \).
\( 6x = 81 \).
Divide both sides by 6: \( x=\frac{81}{6}=13.5 \).

Answer:

A. 13.5