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NO LINKS!! Please help with this problem​

NO LINKS!! Please help with this problem​-example-1

2 Answers

13 votes

Answer:

See below ~

Explanation:

As they are similar, find the scale factor.

  • QR ~ GF
  • 8 : 20
  • 2 : 5

Finding EI

  • ST ~ EI
  • ST : EI = 2 : 5
  • EI = 5 x 12 / 2
  • EI = 30

Finding GH

  • QP : GH = 2 : 5
  • GH = 5 x 12 / 2
  • GH = 30

Finding RS

  • RS : FE = 2 : 5
  • RS = 2 x 25 / 5
  • RS = 10
User Trolologuy
by
7.2k points
6 votes

Answer:

EI = 30

GH = 30

RS = 10

Explanation:

Given: PQRST ~ HGFEI

From inspection of the diagram, the corresponding sides are:

RS ~ FE

ST ~ EI

TP ~ IH

QP ~ GH

QR ~ GF

The only pair of sides that both have side lengths are QR and FG. Therefore, we can use these to work out the scale factor of dilation.

QR = 8 and GF = 20

⇒ GF/QR = 20/8 = 2.5

Therefore, HGFEI is an enlargement of PQRST by a scale factor of 2.5

If ST = 12,

⇒ EI = 12 x 2.5 = 30

If QP = 12,

⇒ GH = 12 x 2.5 = 30

If EF = 25,

⇒ RS = 25 / 2.5 = 10

If IH = 15,

⇒ TP = 15 / 2.5 = 6

User Alan Harper
by
8.7k points

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