Two figures are similar with an area ratio of 25:36. If the perimeter of the larger figure is 42 cm, then what is the perimeter of the smaller figure?

Answer 1

x/42 = 25/36

x/21 = 25/18

x/7 = 25/6

x = 175/6 = 29 1/6 cm = perimeter of smaller figure

Just to check the solution,

try a rectangle LW=36, perimeter=42 =2(L+W)

L=36/W, 21 = L+W = 36/W +W

multiply by W

21W = 36 +W^2

W^2 -21W +36 = 0

W = 21/2 + (1/2)sqr(21^2 -4(36))= 10.5 + (1/2)sqr(441-144) = 10.5 +8.6

W = about 19.1

L= 21-about 19.1 = about 1.9

19.1 x 1.9 = about 36= area of larger figure

for the smaller figure perimeter = 29 1/6 = 2(L+W)

14 7/12 = L+W

L= 175/12 -W

LW= Area = 25

L=25/W

25/W = 175/12 -W multiply by 12W to get

12(25) = 175W -12W^2

12W^2 -175W +300 = 0

W = 175/24 + (1/24)sqr(175^2 -48(300))= about 7.3 + 5.3 = 2

L=25/2 = 12.5

12.5 = 175/12 -2 = 14.6-2 = close to 12.5 with rounding errors