Question

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VWXYZ ~ IJKGH. Find HI, GK, AND JK.

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Answer 1

HI = 35

GK = 45

JK = 25

Explanation:

If VWXYZ ~ IJKGH

Then:

• VW ~ IJ
• WX ~ JK
• XY ~ KG
• YZ ~ GH
• ZV ~ HI

YZ and GH is the only pair of corresponding sides for which we have been given the lengths:

YZ = 36 and GH = 30

Therefore,

VWXYZ : IJKGH = 36 : 30 = 6 : 5

Find HI

ZV : HI = 6 : 5

⇒ 42 : HI = 6 : 5

⇒ 42/HI = 6/5

⇒ 42 · 5 = 6 HI

⇒ HI = 210/6

⇒ HI = 35

Find GK

YX : GK = 6 : 5

⇒ 54 : GK = 6 : 5

⇒ 54/GK = 6/5

⇒ 54 · 5 = 6 GK

⇒ GK = 270/6

⇒ GK = 45

Find JK

WX : JK = 6 : 5

⇒ 30 : JK = 6 : 5

⇒ 30 /JK = 6/5

⇒ 30 · 5 = 6 JK

⇒ JK = 150/6

⇒ JK = 25

Answer 2

HI = 35

GK = 45

JK = 25

Provided:

• VWXYZ ≅ IJKGH

Given proportional sides:

• GH = 30, YZ = 36

Find the scale factor:

• 30/36 = 5/6

Find missing sides:

1) HI = ZV × 5/6 = 42 × 5/6 = 35

2) GK = XY × 5/6 = 54 × 5/6 = 45

3) JK = WX × 5/6 = 30 × 5/6 = 25