The figure shows map of a field bounded by ABCDE. If AB and DE are perpendicular to AE, then the perimeter of the field is

Explanation:

Since AB and DE are perpendicular to AE so AB and DE are perpendicular to BD

Hence ∠CBD = 90^∘ - 30^∘ = 60^∘  

similarly, ∠CDB = 90∘ - 30∘ = 60∘ 

We know that sum of angles of triangle is 180∘ 

So, ∠BCD = 180∘ - (60∘ + 60∘) = 60∘

 Hence \(\triangle\)BCD is equiangle triangle so equilateral triangle,

Now AE||BD so AE = BD = 15 cm

So BC= CD = BD = 15 cm

Also given AB = DE = 15 cm

hence perimeter of ABCDE = 15 + 15 + 15 + 15 + 15 = 75 cm

Option (2) is correct