In the figure given below, ABCD is a square field of area 144 m2, while CEFG is a rectangular field of area 300 m2. If the distance DE is equal to 3 m, then which of the following will be the shortest path to travel from point A to point G?

Question

In the figure given below, ABCD is a square field of area 144 m2, while CEFG is a rectangular field of area 300 m2. If the distance DE is equal to 3 m, then which of the following will be the shortest path to travel from point A to point G?

AEFG
ADEG
ACFG
ABCG

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : ADEG

Given:

ABCD is a square field of area 144 m²

CEFG is a rectangular field of area 300 m²

DE is equal to 3 m

Formula used:

Area of square = (side)²

Area of rectangle = length × breadth

Calculation:

Given, area of square field ABCD = 144 m²

⇒ Side of square field = AB = BC = CD = AD = √144 = 12 m

∵ Diagonal of square = √2 × side

⇒ Diagonal of square field = AC = 12√2 = 12 × 1.414 = 16.97 ≅ 17 m

DE = 3 m,

Using Pythagoras theorem, AE = √(12² + 3²) = √153 = 3√17 ≅ 3 × 4 = 12 m

Breadth of rectangular field CEFG = CE = FG = CD + DE = 12 + 3 = 15 m

Area of rectangular field = 300 m²

⇒ Length of rectangular field CEFG = EF = CG = 300/15 = 20 m

⇒ Diagonal of rectangular field = CF = EG = √(20² + 15²) = √625 = 25 m

Now,

Length of path AEFG = AE + EF + FG = 12 + 20 + 15 = 47 m

Length of path ADEG = AD + DE + EG = 12 + 3 + 25 = 40 m

Length of path ACFG = AC + CF + FG = 17 + 25 + 15 = 57 m

Length of path ABCG = AB + BC + CG = 12 + 12 + 20 = 44 m

∴ Path ADEG is the shortest path