Effect of scale factor on similar figures. Game on.

Effect of scale factor on similar figures is a grade 7 math skill aligned to Common Core standard 7.G.A.1. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 effect of scale factor on similar figures problems our math games drill.

CCSS 7.G.A.110 questions in the bank
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Warm-upeasy

Rectangles JKLMJKLM and NPQRNPQR are similar. The perimeter of rectangle JKLMJKLM is 18,18\textsf{,} and the perimeter of rectangle NPQRNPQR is 45.45\textsf{.} Side JKJK corresponds to side NP,NP\textsf{,} and JK=6.JK = 6\textsf{.} What is the length of NP?NP\textsf{?}

The scale factor from rectangle JKLMJKLM to rectangle NPQRNPQR equals the perimeter ratio 4518=52.\dfrac{45}{18} = \dfrac{5}{2}\textsf{.} So NP=6⋅52=15.NP = 6 \cdot \dfrac{5}{2} = 15\textsf{.}

Mid-gameeasy

Similar triangles GHIGHI and JKLJKL have perimeters 1616 and 48.48\textsf{.} Side GHGH corresponds to side JK,JK\textsf{,} and GH=5.GH = 5\textsf{.} What is the length of JK?JK\textsf{?}

The scale factor from △GHI\triangle GHI to △JKL\triangle JKL is 4816=3.\dfrac{48}{16} = 3\textsf{.} Corresponding sides scale by 3,3\textsf{,} so JK=5⋅3=15.JK = 5 \cdot 3 = 15\textsf{.}

Mid-gameeasy

Pentagons ABCDEABCDE and FGHJKFGHJK are similar. The perimeter of pentagon ABCDEABCDE is 35,35\textsf{,} and the perimeter of pentagon FGHJKFGHJK is 21.21\textsf{.} Side ABAB corresponds to side FG,FG\textsf{,} and AB=20.AB = 20\textsf{.} What is the length of FG?FG\textsf{?}

The scale factor from pentagon ABCDEABCDE to pentagon FGHJKFGHJK is 2135=35.\dfrac{21}{35} = \dfrac{3}{5}\textsf{.} So FG=20⋅35=12.FG = 20 \cdot \dfrac{3}{5} = 12\textsf{.}

Mid-gameeasy

Similar triangles RSTRST and UVWUVW have perimeters 2828 and 42.42\textsf{.} Side RSRS corresponds to side UV,UV\textsf{,} and RS=10.RS = 10\textsf{.} What is the length of UV?UV\textsf{?}

The scale factor from △RST\triangle RST to △UVW\triangle UVW is 4228=32.\dfrac{42}{28} = \dfrac{3}{2}\textsf{.} So UV=10⋅32=15.UV = 10 \cdot \dfrac{3}{2} = 15\textsf{.}

Mid-gameeasy

Similar rectangles WXYZWXYZ and ABCDABCD have areas 1616 and 64.64\textsf{.} Side WXWX corresponds to side AB,AB\textsf{,} and WX=5.WX = 5\textsf{.} What is the length of AB?AB\textsf{?}

The area ratio is 6416=4=k2,\dfrac{64}{16} = 4 = k^{2}\textsf{,} so the scale factor is k=2.k = 2\textsf{.} Then AB=5⋅2=10.AB = 5 \cdot 2 = 10\textsf{.}

Mid-gameeasy

Parallelograms EFGHEFGH and JKLMJKLM are similar. The area of parallelogram EFGHEFGH is 9,9\textsf{,} and the area of parallelogram JKLMJKLM is 36.36\textsf{.} Side EFEF corresponds to side JK,JK\textsf{,} and EF=7.EF = 7\textsf{.} What is the length of JK?JK\textsf{?}

The area ratio is 369=4=k2,\dfrac{36}{9} = 4 = k^{2}\textsf{,} so k=2.k = 2\textsf{.} Then JK=7⋅2=14.JK = 7 \cdot 2 = 14\textsf{.}

Mid-gameeasy

Similar triangles MNOMNO and PQRPQR have areas 44 and 36.36\textsf{.} Side MNMN corresponds to side PQ,PQ\textsf{,} and MN=5.MN = 5\textsf{.} What is the length of PQ?PQ\textsf{?}

The area ratio is 364=9=k2,\dfrac{36}{4} = 9 = k^{2}\textsf{,} so k=3.k = 3\textsf{.} Then PQ=5⋅3=15.PQ = 5 \cdot 3 = 15\textsf{.}

Buzzer beatereasy

Similar triangles STUSTU and VWXVWX have areas 3636 and 9.9\textsf{.} Side STST corresponds to side VW,VW\textsf{,} and ST=12.ST = 12\textsf{.} What is the length of VW?VW\textsf{?}

The scale factor from △STU\triangle STU to △VWX\triangle VWX satisfies k2=936=14,k^{2} = \dfrac{9}{36} = \dfrac{1}{4}\textsf{,} so k=12.k = \dfrac{1}{2}\textsf{.} Then VW=12⋅12=6.VW = 12 \cdot \dfrac{1}{2} = 6\textsf{.}

Overtime

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Tests that cover effect of scale factor on similar figures:
NAEPSBACPSAT 8/9NC EOG/EOCVTCAP
More Grade 7 skills
Compound probabilityPercent proportion word problemsSolving one- and two-step linear equationsCircle formulasCombining like terms and distributingComparing mediansMake devices fair from experimental resultsPercent problemsAll Grade 7 practice →

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