Question

a rectangular park is of dimensions 32/3 m ×58/5 m. Two cross roads, each of width 2 1/2 m, run at right angles through the centre of the park such that each is parallel to one of the two sides of the park. Find the total area occupied by the roads.​

Answer 1

Given :- a rectangular park is of dimensions 32/3 m ×58/5 m. Two cross roads, each of width 2 1/2 m, run at right angles through the centre of the park such that each is parallel to one of the two sides of the park.

To Find :-

• Find the total area occupied by the roads.

Answer :-

we know that,

• Area of rectangle = length * breadth
• Area of square = (side)² .

now, first road is parallel to length .

so,

→ Length of first road = Length of rectangle = (32/3) m

→ Breadth of road = width = 2(1/2) = (5/2) m .

then,

→ Area of first road = L * B = (32/3) * (5/2) = (80/3) m² .

similarly, second road is parallel to breadth .

→ Length of second road = Breadth of rectangle = (58/5) m

→ Breadth of road = width = 2(1/2) = (5/2) m .

then,

→ Area of second road = L * B = (58/5) * (5/2) = 29 m² .

also,

→ Common area between both roads = in the shape of square of side equal to width = (5/2)² = (25/4) m²

then,

→ Total area of both roads = Area of first road + Area of second road - common area

→ Total area = (80/3) + 29 - (25/4) = (80 * 4 + 29 * 12 - 25*3)/12 = (320 + 348 - 75)/12 = (668 - 75)/12 = 593/12 = 49(5/12) m (Ans.)

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Answer 2

Step-by-step explanation:

Given,

A rectangular lawn 60 meters by 40 meters has two roads each 5 meters wide running in the middle of it one parallel to length and the other parallel to breadth

Area of the road=40×5+60×5−5×5

=200+300−25

=475sqm

Given,

Cost of graveling the roads =60 paise per sq meter.

∴475×60paise

=28500 paise

=Rs.285