Teacher's Guide - Pearson

4.R915S12TRSRatio of sides___DE ​ 5 ​ 9__3 ​ 5 3 ___ STEF ​ 5 ___ ​ 124 ​ 5 3 ___ RTDF ​ 5 ___ ​ 155 ​ 5 3perimeter RSTRatio of perimeters ______________perimeter of DEF ​ 5 ___ ​ 3612 ​ 5 3area of RSTRatio of areas__________area of DEF ​ 5 ___ ​ 546 ​ 5 95. The ratios of the lengths of the sides are equal, because the triangles are similar.The ratios of the perimeters are the same, because the perimeters are the sum ofthe sides.The ratio of the areas is the same, because the ratio of the perimeters are equal;and the ratio of the areas is a square, because length 3 length is a square.Activity 12.1 (Student’s Book page 213)​ ​ ​ 1. Perimeter of rectangle ABCD 5 2(3 1 10) 5 26 cmArea of rectangle ABCD is 3 3 10 5 30 cm 2Perimeter of MNOP 5 2(4.2 1 14) 5 36.4Area of MNOP 5 58.8 cm 2Ratio of length 5 ___ 147__ 7__5 ​10 5Ratio of side 5 ___ 1410 5 7__5 ​ Ratio of perimeters ____ 36.426____ 364260Ratio of areas 58.85 ____30 5 ____ 588300___ 4921 (​ 7__5 ​)22. a) TrianglesRatio of the sides is 1:3 Ratio of perimeters is 1:3 Ratio of areas is 1:9b) RectanglesRatio of sides is 2:3 Ratio of perimeters is 2:3 Ratio of areas is 4:9c) ArrowsRatio of sides 7:4 Ratio of perimeters is 7:4 Ratio of areas is 49:16Extension Activity 12.1 (Student’s Book page 214)Ratio of perimeters 5 3:4, therefore ratio of areas is 9:16.The sum of the areas is 75 cm 2 .9The area of the smaller triangle is 75 3 (​ ___25 ​) 5 27 cm2 .16The area of the larger triangle is 75 3 (​ ___25 ​) 5 48 cm2 .66 EXPLORING MATHEMATICS FORM 3