Answer
By applying the theorems of triangle similarity, we find that GF measures 16 cm (the fourth option). Here’s the breakdown: Since S and T are the midpoints of triangle FGH’s sides, line segment ST is parallel to side GF; thus, triangles FGH and TSH are similar, ensuring corresponding sides maintain proportionality. Therefore, we have GF/ST = FH/TH = GH/SH. Given that FT equals 6 cm (as T is the midpoint of FH), it follows that FH is 12 cm since FH = 2 TH = 2 FT = 2(6 cm). Point GS measures 4 cm, leading to SH also being 4 cm (as S is the midpoint of GH), leading to GH being 8 cm, since GH = 2 GS = 2 SH = 2(4 cm). The length of ST is confirmed as 8 cm. Inputting known values into the proportion: GF/(8 cm) = (12 cm)/(6 cm) = (8 cm)/(4 cm), we find GF/(8 cm) = 2. Thus, solving for GF results in GF = 16 cm after multiplying both sides by 8 cm.
Related Questions
- What should the exponent of the variable b be in Marina’s simplified expression (-frac{1}{2}a^4b)
- Using the words from the word list, name all the parts of an isosceles triangle. Some words may be u
- Naoya read a book cover to cover in a single session at a rate of 55 pages per hour. After 4 hours,
- What are the expected total number of orange candies and the standard deviation for the total number
- What equation represents the transformed function of the graph y = |x| as shown below?
- Which statement describes whether there is an extraneous solution to the equation x – 3 = x – 5? A.
- In rectangle JKLM, with m∠KJM = m∠KLM = 90° and m∠KJC + m∠MLC, which reason justifies the s
- What do the properties of polynomial addition mean? Complete each statement: The closure property st
- Dan uses a compass to draw an arc from point Q, as shown. He wants to construct a line segment throu
- A company manufactures video games with a current defect rate of 0.95%. To minimize the number of de