Question

. The perimeter of a triangular field is 90m and the length of its two sides are 41 m and 40 m.Find the number of rose bed that can be prepared in the field if each rose bed on an average needs 900 sq cm space.

Answer 1

Answer:

• 2000 rose beds can be placed in the triangular field .

Step-by-step explanation:

• Perimeter of triangular field is 90 m

• two of its sides are 41 m and 40 m

so,

→ length of third side = 90 -  ( 41 + 40 ) = 9 m

so, three sides of triangle are

→ a = 41 m , b = 40 m and c = 9 m

Now,

Calculating semi-perimeter of triangular field

→ semi perimeter, s = ( 90 ) / 2 = 45 cm

Using herons formula to calculate area of triangular field

→ ar(triangular field) = √[ s ( s - a ) ( s - b ) ( s - c ) ]

→ ar(triangular field) = √[(45) (45-41) (45-40) (45-9)]

→ ar ( field ) = √( 45 × 4 × 5 × 36 )

→ ar (field) = 180 m²

Now,

since, each rose bed need 900 cm² area

means each rose bed need 900 × 10⁻⁴ m² area

therefore,

→ No. of rose beds can be placed = ( area of field ) / ( area needed for each rose bed )

→ no. of rose beds can be placed = 180/(900×10⁻⁴)

→ no. of rose beds can be placed = 2000

therefore,

• 2000 rose beds can be placed in the triangular field .