Question

Points S and T are midpoints of the sides of triangle FGH

what is GF ?

Answer 1

Answer:

Using triangle similarity theorems, GF is 16 cm (fourth option)

Step-by-step explanation:

If points S and T are midpoints of the sides of triangle FGH, the segment ST is parallel to the side GF and the triangles FGH and TSH are similars, and their corresponding sides must be proportionals, then:

GF/ST=FH/TH=GH/SH

TH=6 cm→FT=6 cm, because T is the midpoint of side FH, and:

FH=2 TH = 2 FT =2 (6 cm)→FH=12 cm

GS=4 cm→SH=4 cm, because S is the midpoint of side GH, and:

GH=2 GS = 2 SH =2 (4 cm)→GH=8 cm

ST= 8 cm

Replacing the known values in the proportion:

GF/ST=FH/TH=GH/SH

GF/(8 cm)=(12 cm)/(6 cm)=(8 cm)/(4 cm)

GF/(8 cm)=2=2

GF/(8 cm)=2

Solving for GF: Multiplying both sides of the equation by 8 cm:

(8 cm) [GF/(8 cm)]=(8 cm)(2)

GF=16 cm

Answer 2

If Points S and T are midpoints of the sides of triangle FGH, the measure of the length GF is 16cm. Option D is correct

To get the length of Gf, we will need to use the similarity theorem of a triangle as shown:

HT/TS = HF/Gf

From the diagram, we have the following:

HT = FT = 6cm

ST = 8cm

Substitute the given parameters into the formula to have:

6/8 = 6+6/GF

6/8 = 12/GF

6FG = 96

FG = 96/6

FG = 16cm

Hence the measure of the length GF is 16cm

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